You ask an LLM: "What's 17 × 24?"

A basic model might output 408—correct, but how? Did it multiply step-by-step? Did it retrieve a memorized pattern? Or did it get lucky with token prediction?

Now ask: "A train leaves Chicago at 9 AM traveling at 60 mph. Another train leaves New York at 10 AM traveling at 80 mph toward Chicago. If the cities are 800 miles apart, when do the trains meet?"

This requires actual reasoning: setting up equations, tracking multiple variables, performing sequential calculations. An LLM that just predicts the "most likely next token" shouldn't be able to solve this.

Yet modern LLMs can.

Understanding how they do it—and how to make them do it better—is essential for anyone building AI systems that need to think, not just respond.

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The Paradox: Prediction vs. Reasoning

Here's the fundamental tension: LLMs are trained to predict the next token. That's it. There's no explicit "reasoning module" in a Transformer architecture. Every output is a probability distribution over the vocabulary, conditioned on everything that came before.

So how does a prediction machine perform logical reasoning?

The Breakthrough Insight: Reasoning as Sequential Prediction

The key realization is that reasoning steps can be externalized as tokens. When humans solve complex problems, we think out loud—we write intermediate steps, check our work, backtrack when stuck. LLMs can do the same thing, but in their "language": tokens.

Consider two approaches to the same math problem:

Direct prediction:

Reasoning as tokens:

In the second case, each intermediate step becomes part of the context for the next prediction. The model isn't "thinking" in some abstract sense—it's generating tokens that happen to represent reasoning steps, and those tokens influence subsequent generations.

This is chain-of-thought (CoT) reasoning, and it's the foundation of everything that follows.

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Chain-of-Thought: Teaching LLMs to Show Their Work

The Discovery

In 2022, Google researchers made a striking observation: simply asking an LLM to "think step by step" dramatically improved performance on reasoning tasks. On the GSM8K math benchmark, adding chain-of-thought prompting improved accuracy from 17.1% to 58.1%—a 3x improvement from just changing the prompt.

Why Does This Work?

Three mechanisms explain chain-of-thought effectiveness:

1. Working Memory Expansion

An LLM's context window is its only "memory" during generation. By externalizing intermediate steps as tokens, the model creates a form of working memory. Each reasoning step is preserved in context, available for the model to reference when generating the next step.

2. Problem Decomposition

Complex problems that exceed the model's single-pass capacity become solvable when broken into simpler subproblems. Each subproblem is easier to solve, and the chain of solutions builds toward the final answer.

3. Error Exposure

When reasoning is explicit, errors become visible—both to the model (which can potentially self-correct) and to the observer (who can identify where reasoning went wrong). This is crucial for debugging and improvement.

The Prompting Spectrum

Chain-of-thought exists on a spectrum from implicit to explicit:

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The Architecture Shift: Reasoning Models

Chain-of-thought prompting extracts reasoning from models that weren't explicitly trained for it. But what if you trained a model specifically for reasoning?

This is the insight behind reasoning models like OpenAI's o1 series and Anthropic's extended thinking in Claude.

How Reasoning Models Differ

Traditional LLMs optimize for:

Given input X, generate the most likely output Y in minimal tokens.

Reasoning models optimize for:

Given problem X, generate whatever reasoning is needed to arrive at correct answer Y.

The key difference is test-time compute—the computational resources spent during inference. A reasoning model might generate thousands of internal tokens exploring a problem before producing its answer.

The Test-Time Compute Paradigm

Consider this trade-off:

Reasoning models can adaptively allocate more "thinking time" to harder problems. A simple question gets a quick answer; a complex proof gets extended deliberation.

What Happens Inside a Reasoning Model?

When you query a reasoning model like o1 with a complex problem:

1. Problem Analysis: The model generates tokens that decompose the problem structure
2. Strategy Selection: It explores potential approaches (often multiple in parallel)
3. Execution: It works through the chosen strategy step-by-step
4. Verification: It checks intermediate results for consistency
5. Backtracking: If an approach fails, it returns to explore alternatives
6. Synthesis: It combines results into a final answer

All of this happens as token generation—but the tokens are optimized for reasoning quality, not just likelihood.

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From Reasoning to Reasoning Agents

A reasoning model can think through problems. But it operates in isolation—given a question, it reasons to an answer. What if we want AI that can:

• Interact with the world to gather information
• Take actions based on its reasoning
• Iterate until a goal is achieved
• Handle multi-step tasks autonomously

This is a reasoning agent.

What Makes Something a Reasoning Agent?

A reasoning agent combines three capabilities:

1. Reasoning (The "Brain")

The core LLM provides the reasoning capability—the ability to plan, decompose problems, make decisions, and synthesize information. This is where chain-of-thought and reasoning model architectures pay off.

2. Tool Use (The "Hands")

The agent can interact with external systems:

• Information retrieval: Search databases, query APIs, browse the web
• Computation: Execute code, run calculations, transform data
• Actions: Send messages, create files, modify records

Tools extend the agent's capabilities beyond pure language generation.

3. Feedback Loops (The "Learning")

After taking an action, the agent observes the result and adjusts:

• Did the retrieved information help? If not, try different queries
• Did the code execute correctly? If not, debug and retry
• Is the goal achieved? If not, continue planning

This observe-act-evaluate loop enables multi-step problem solving.

The Reasoning Agent Loop

Reasoning Agents in Practice

Example: Autonomous Code Debugging

User: "Fix the bug in our payment processing module"

Traditional chatbot: "Here are some common payment bugs: 1) decimal precision errors, 2) race conditions..."

Reasoning agent:

1. Reason: "I need to understand the codebase structure and find the payment module"
2. Act: Search codebase for payment-related files
3. Observe: Found payment_processor.py, billing_service.py, and related tests
4. Reason: "Let me examine the payment processor for obvious issues"
5. Act: Read payment_processor.py
6. Observe: Found potential issue—currency conversion happens after validation
7. Reason: "This could cause validation to pass for invalid amounts. Let me check the test coverage"
8. Act: Read and run relevant tests
9. Observe: Tests don't cover currency conversion edge cases
10. Reason: "I've identified the bug. I should fix it and add tests"
11. Act: Generate fix and new tests
12. Return: "Fixed currency conversion bug in payment_processor.py. The issue was [detailed explanation]. Added 3 new test cases."

This is the pattern that enables agentic AI systems to accomplish real work.

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The Technical Mechanisms Behind Reasoning

Attention and Reasoning Depth

The Transformer's attention mechanism is central to reasoning. Each token can attend to all previous tokens, allowing information to flow from reasoning steps to conclusions.

Key insight: Reasoning depth is limited by attention span. A complex derivation requiring 20 logical steps needs all 20 steps in context for the conclusion to be properly conditioned.

This is why longer reasoning chains often produce better results—more intermediate steps means more information available in context when generating the answer.

Emergent vs. Trained Reasoning

Emergent reasoning appears in models trained purely on next-token prediction, seemingly "for free." GPT-4 can solve logic puzzles it was never explicitly trained on.

Trained reasoning is explicitly optimized. o1-style models are trained with reinforcement learning to produce reasoning chains that lead to correct answers, not just likely token sequences.

The distinction matters:

• Emergent reasoning is brittle and inconsistent
• Trained reasoning is more reliable but requires specialized training infrastructure

The Role of Scale

Reasoning capabilities improve dramatically with scale, but not linearly:

The jump from "can do simple reasoning" to "can solve novel complex problems" requires both scale and architectural/training innovations.

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Limitations and Failure Modes

Understanding how reasoning fails is as important as understanding how it works.

Common Failure Modes

1. Plausible-Sounding Nonsense

LLMs can generate reasoning chains that look correct but contain logical errors. The model optimizes for "sounds like good reasoning" which isn't the same as "is good reasoning."

The reasoning is correct here, but the model might generate equally confident-looking chains that are wrong.

2. Reasoning Chain Derailment

Long reasoning chains can go off track. An error in step 3 propagates through steps 4-10, leading to confident wrong answers.

3. Knowledge vs. Reasoning Confusion

Models sometimes substitute memorized facts for actual reasoning:

This matters when the question is slightly different from training examples.

4. Sycophancy in Reasoning

Models may adjust their reasoning to match what they think the user wants to hear, rather than what's logically correct.

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Building Effective Reasoning Systems

Prompting Best Practices

1. Be explicit about reasoning requirements:

2. Provide reasoning structure:

3. Request verification:

Architectural Patterns for Reasoning Agents

1. Tool abstraction layer: Don't give agents raw API access. Create well-defined tool interfaces with clear inputs, outputs, and constraints.

2. Scratchpad memory: Maintain a working memory where the agent can record intermediate results, hypotheses, and observations.

3. Verification loops: After critical reasoning steps, explicitly prompt the model to verify before proceeding.

4. Graceful degradation: When reasoning fails or confidence is low, escalate to human review rather than proceeding with uncertain results.

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Key Takeaways

• Reasoning in LLMs is externalized as tokens—chain-of-thought turns internal computation into explicit text
• Test-time compute is the new frontier—reasoning models allocate more inference-time processing to harder problems
• Reasoning agents combine thinking with action—they plan, execute, observe, and iterate toward goals
• Scale and training both matter—large models show emergent reasoning; specialized training makes it reliable
• Failure modes are predictable—plausible-sounding errors, chain derailment, and sycophancy are common pitfalls
• Structure improves reasoning—explicit prompts, verification steps, and tool abstractions make reasoning more reliable

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The evolution from "LLMs that predict tokens" to "reasoning agents that solve problems" represents one of the most significant capability jumps in AI. Understanding how reasoning actually works—not as magic, but as structured token generation—is essential for anyone building systems that need to think.

The next frontier isn't just making models bigger. It's making them better at reasoning when it counts.

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