models · Level 4
Reasoning models and reasoning engines
How models that think before they answer work, when they pay off, and how they differ from classical rule-based reasoning.
Start with the essentials
The short answer
A reasoning model is a language model built to spend extra computation working through a problem, in a long chain of intermediate steps, before it gives a final answer. It helps most on multi-step maths, code and planning, and costs more time and money on simple questions. Its visible working is not necessarily a faithful account of why it answered as it did.
What you will learn
- You will be able to explain what a reasoning model is, and what chain of thought and test-time compute mean.
- You will be able to decide when a reasoning model is worth its extra time and cost, and when it is not.
- You will know how to control reasoning effort and how to prompt reasoning models well.
- You will understand why a visible reasoning trace is not necessarily a faithful explanation.
- You will be able to design simple verifiers and generate-and-check loops around a model.
- You will be able to explain classical inference engines, forward and backward chaining, and neuro-symbolic hybrids.
Who it is for
Readers who already use language models and want to know what changes when a model thinks before it answers. No coding is needed, though one chapter includes a short code sketch.
Before you start
- Comfort with tokens, prompts and context windows (see What is AI?).
- Access to any reasoning-capable model or service with an adjustable setting is helpful for the exercises.
Keep learning
The complete workbook
This workbook explains what reasoning models are and how they are trained and used. You will learn when extra thinking helps and when it wastes money, how to control reasoning effort, and why a reasoning trace should not be treated as proof. It also covers the older meaning of reasoning engine in symbolic AI, and how the two are combined in neuro-symbolic systems.
- 01What a reasoning model isIn the workbook · 1 exercise
Some models start answering at once. Others are built to work through the problem first. The difference is where the computation goes.
- 02When reasoning helps, and when it does notIn the workbook · Reading
A reasoning model is a tool with a price. Use it where the price buys something.
- 03Controlling reasoning effort, and prompting wellIn the workbook · 1 exercise
Most reasoning services give you a dial. Turn it deliberately.
- 04Why the trace is not the explanationIn the workbook · 1 exercise
Many reasoning models show their working. It is tempting to read it as a window into the model's mind. Be careful.
- 05Verifiers and checkingIn the workbook · Reading
The most reliable way to use a reasoning model is to pair it with something that checks.
- 06The other reasoning engine: rules, and hybridsIn the workbook · 1 exercise
Long before language models, an inference engine or reasoning engine meant something quite different.
Also inside: a 9-point checklist, a glossary of 12 terms and 10 questions and answers to test yourself. 4 hands-on exercises, each with a worked answer at the back where the workbook gives one.
No login, no card, no account. Before the download we ask you to follow Mickai (two quick links). Free to download and use for personal learning, study groups and inside your own team. Please do not resell the workbooks or republish them as your own. Link people to trust-agent.ai instead.
Test yourself
Questions and answers
What is a reasoning model?
A language model trained to spend extra computation working through a problem, usually in a long chain of intermediate steps, before it gives a final answer. It tends to do better on multi-step maths, code and planning, and it is slower and costlier than an ordinary chat model.
How are reasoning models trained?
Published descriptions commonly involve reinforcement learning: the model attempts many problems and is rewarded when the final answer is correct, on tasks that can be checked automatically. Over training it tends to learn longer working and self-checking. Exact recipes differ and are not always published.
What is test-time compute?
It is the computation used while a model is answering rather than while it is trained. Letting a model think longer spends more of it. A 2024 study found that, on problems a smaller model could already sometimes solve, spending it well could beat a much larger model, but not on the hardest problems.
When should I use a reasoning model?
Use one for multi-step maths and logic, tricky code and debugging, and planning with constraints, especially when you can check the answer. Avoid it for simple chat, rewriting, summarising and lookups, where it adds delay and cost for little gain.
Why not use a reasoning model for everything?
Because thinking costs time and money. Many hosted services bill thinking tokens as output tokens, so an easy question can become expensive for no benefit. Routing easy work to a fast model and hard work to a reasoning model is usually sensible.
What does reasoning effort control?
It sets how much thinking the model does before answering. Providers offer on and off switches, named levels, numeric scales or token caps. Higher effort usually means slower and costlier replies. Start low and raise it only when your checks fail.
Can I trust the reasoning trace as an explanation?
Not on its own. Studies have found that chain-of-thought explanations can be influenced by factors they never mention, and can rationalise wrong answers. Use traces to spot errors, and verify answers with independent checks rather than relying on the model's account.
What is a verifier?
A verifier is anything that judges whether an answer is acceptable: running tests, validating a schema, recomputing totals, a second model scoring against a rubric, or a person. Pairing a model with a verifier is one of the most reliable ways to use it.
What is an inference engine in classical AI?
It is software that applies logical rules to a knowledge base of facts to derive new conclusions, using strategies such as forward and backward chaining. Expert systems used this approach. It is unrelated to the software that runs a neural network.
What is a neuro-symbolic system?
One that combines neural networks with symbolic rules or logic. A typical pattern lets a model read messy input and produce structured facts, then lets a rule engine or solver make the exact, explainable decision.
When you have finished
Get your certificate of completion
Type your name and download a certificate for this workbook as a PDF, ready to print or to add to LinkedIn. It is made on your own device, so your name is never sent to us. It is a self-declared certificate, not an accredited qualification.
Learn the language
Key terms
- Reasoning model
- A language model trained to spend extra computation working through a problem in a chain of steps before giving its answer.
- Chain of thought
- A series of intermediate steps written out before a final answer.
- Test-time compute
- Computation spent while a model is answering, rather than while it was being trained.
- Reasoning trace
- The visible working a reasoning model produces before its answer.
- Reasoning effort
- A setting that controls how much thinking a model does before answering, such as levels, a scale or a token cap.
- Reinforcement learning
- Training by trial and reward, where a model is rewarded for outcomes such as a correct final answer.
6 of the workbook's 12 terms. The complete glossary is in the workbook.
Follow the evidence
Sources and checks
Facts last checked: .
These workbooks use AI assistance. See how the workbooks are made.
- Chain-of-Thought Prompting Elicits Reasoning in Large Language ModelsarXiv, 2201.11903
- Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model ParametersarXiv, 2408.03314
- Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language ModelsarXiv, 2501.09686
- Training Verifiers to Solve Math Word ProblemsarXiv, 2110.14168
- Self-Consistency Improves Chain of Thought Reasoning in Language ModelsarXiv, 2203.11171
- Let's Verify Step by SteparXiv, 2305.20050
- Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought PromptingarXiv, 2305.04388
- Reasoning Models Don't Always Say What They ThinkarXiv, 2505.05410
- Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AIarXiv, 2401.01040
- Artificial Intelligence: A Modern Approach (chapters on logical agents and inference)Russell and Norvig, book website, UC Berkeley
- AIMA pseudocode: forward-chaining and backward-chaining algorithmsaimacode, GitHub
- DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement LearningarXiv, 2501.12948
- Reasoning models (how reasoning tokens are billed)OpenAI API documentation
- Gemini thinking (pricing of thinking tokens)Google AI for Developers
Created by Mickarle Wagstaff-Irons - Micky Irons with the Mickai team. Published by Mickai LTD. Last updated 25 September 2026.
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