Chain-of-Thought — Step-by-step reasoning

Section 10.2.4 : Chain-of-Thought — Step-by-step reasoning

🎯 Learning objective

Mastering Chain-of-Thought (CoT) prompting to obtain structured reasoning and more reliable answers on complex problems requiring multi-step thinking. This is the technique that has most improved LLM reasoning capabilities.

The problem: LLMs and reasoning

LLMs excel at text generation but struggle with problems requiring multi-step logical reasoning: calculations, problem-solving, comparative analyses, planning. Why? They predict the next token — they don't naturally "think" step by step. They "think while writing," not "think then write."

Chain-of-Thought prompting (Wei et al., Google Brain, 2022) solves this problem elegantly: by explicitly asking the model to show its reasoning before giving its answer, we force a decomposition that radically improves quality.

The 3 variants of Chain-of-Thought

1. Zero-shot CoT: the magic method (the simplest)

Simply add a "magic" phrase at the end of your prompt. This is the technique with the best effort/result ratio in all of prompt engineering.

Without CoT:

If a train leaves Paris at 2:00 PM at 300 km/h and another 
leaves Lyon (450 km from Paris) at 2:30 PM at 250 km/h toward Paris, 
what time do they cross?

→ "They cross at about 3:00 PM." (often wrong)

With CoT (zero-shot):

If a train leaves Paris at 2:00 PM at 300 km/h and another 
leaves Lyon (450 km from Paris) at 2:30 PM at 250 km/h toward Paris, 
what time do they cross?

Think step by step before giving your answer.

→ The model decomposes: 
  1. Train 1 position at 2:30 PM: 300 × 0.5 = 150 km from Paris
  2. Remaining distance between the two trains: 450 - 150 = 300 km
  3. Closing speed: 300 + 250 = 550 km/h
  4. Time to cross: 300 / 550 ≈ 0.545h ≈ 32 min 44 sec
  5. Crossing time: 2:30 PM + 32min44s ≈ 3:03 PM

CoT magic phrases (all work, choose the one that suits you):

2. Few-shot CoT: reasoning guided by example

For recurring problems, provide examples with the complete reasoning:

Solve these SaaS pricing problems by showing your complete reasoning.

Problem: A SaaS at €49/month has 200 customers. If we increase 
the price by 20%, we lose 15% of customers. Should we increase?

Reasoning:
- Current revenue: 49 × 200 = €9,800/month
- New price: 49 × 1.2 = €58.8 → rounded to €59/month
- Remaining customers: 200 × 0.85 = 170 customers
- New revenue: 59 × 170 = €10,030/month
- Difference: +€230/month (+2.3%)
- But: 30 lost customers = 30 fewer contracts for the future
- Conclusion: YES financially in the short term, but evaluate 
  the impact on churn and word-of-mouth.

Problem: A freelancer charges €500/day and works 20 days/month.
An AI tool at €200/month saves them 2 days/month of billable work.
Should they adopt it?

Reasoning:

3. Structured CoT: imposing a reasoning structure

For complex analyses, impose the steps:

Analyze this investment decision following 
these 5 MANDATORY steps:

STEP 1 — DATA: List all quantitative data 
available in the problem.
STEP 2 — ASSUMPTIONS: Identify implicit assumptions 
and their credibility (strong/medium/weak).
STEP 3 — CALCULATIONS: Perform calculations step by step.
STEP 4 — ANALYSIS: Identify strengths and risks.
STEP 5 — CONCLUSION: Give your recommendation with 
confidence level (1-10).

[Investment description]

Professional applications of CoT

Business analysis

Our landing page conversion rate dropped from 3.2% to 1.8% this month.

Reason step by step to identify the causes:
1. Start with the most likely causes (traffic, offer, technical)
2. For each hypothesis, indicate how to verify it
3. Rank hypotheses by probability
4. Recommend 3 immediate actions in order of priority

Weighted decision-making

I need to choose between 3 AI providers for my company.
Reason step by step using a weighted decision matrix.

Criteria (with weights):
- Price (30%)
- Performance (25%)
- Customer support (20%)
- Ease of integration (15%)
- Scalability (10%)

Provider A: [details]
Provider B: [details]
Provider C: [details]

For each provider, rate each criterion from 1 to 10, 
then calculate the weighted score.

Estimation (Fermi technique)

Estimate the number of pizzas consumed in France per day.

Reason step by step with Fermi estimates:
1. French population
2. % who eat pizza in a given week
3. Average frequency
4. Distribution by day
5. Result with high/low range

When NOT to use CoT

Practical exercise

Duration: 15 minutes

1. →Take a real professional problem (budget allocation, vendor selection, market size estimation)
2. →Ask it without CoT → note the quality and depth
3. →Add "Think step by step" → compare
4. →Try structured CoT by imposing 5 steps → compare again