10.2. Chain-of-Thought & Reasoning Prompts

10.2.1. Why Reasoning Matters in Prompts

Standard prompts ask the model to jump straight from input to answer. For tasks that require multi-step logic — mathematics, causal reasoning, multi-hop question answering — this direct approach frequently fails. Chain-of-Thought (CoT) prompting addresses this by eliciting an explicit reasoning trace before the final answer.

The core insight (Wei et al., 2022): if you give a large-enough model room to “think aloud”, its accuracy on hard reasoning tasks improves dramatically. The reasoning steps serve as scratchpad space and also let you verify the model’s logic.

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10.2.2. Zero-Shot Chain-of-Thought

The simplest activation: append “Let’s think step by step.” to any question. No examples needed.

import anthropic

client = anthropic.Anthropic()

def prompt(system: str, user: str, max_tokens: int = 600) -> str:
    msg = client.messages.create(
        model="claude-sonnet-4-6",
        max_tokens=max_tokens,
        system=system,
        messages=[{"role": "user", "content": user}]
    )
    return msg.content[0].text


question = """A store sells apples at 3 for €2.
Maria buys 15 apples and pays with a €20 note.
How much change does she receive?"""

# Direct answer
direct = prompt("Answer concisely.", question)
print(f"Direct: {direct}")

# Zero-Shot CoT
cot = prompt(
    "Answer the question. Let's think step by step.",
    question
)
print(f"\nZero-Shot CoT:\n{cot}")

Direct: €10

Zero-Shot CoT:
Step 1: Find the price per apple.
        3 apples = €2 → 1 apple = €2/3

Step 2: Cost of 15 apples.
        15 × (€2/3) = €30/3 = €10

Step 3: Change from €20.
        €20 − €10 = €10

Answer: Maria receives €10 change.

Note

Zero-Shot CoT works because large models already know how to reason — the trigger phrase simply shifts them from “answer immediately” mode to “explain your reasoning” mode.

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10.2.3. Few-Shot Chain-of-Thought

Provide worked examples that include both the reasoning trace and the final answer. The model learns the expected reasoning pattern from the demonstrations.

FEW_SHOT_COT = """Solve each problem by thinking step by step, then state the answer.

Problem: A cyclist travels 60 km in 2 hours, then rests for 30 minutes,
         then travels 40 km in 1 hour. What is the average speed for the
         entire journey (excluding rest time)?
Reasoning:
  Total distance = 60 + 40 = 100 km
  Total moving time = 2 h + 1 h = 3 h
  Average speed = 100 / 3 ≈ 33.3 km/h
Answer: ≈ 33.3 km/h

Problem: A tank is 3/4 full. After adding 120 litres it is 9/10 full.
         What is the tank's total capacity?
Reasoning:
  The 120 litres represent 9/10 − 3/4 = 18/20 − 15/20 = 3/20 of the tank.
  Total capacity = 120 / (3/20) = 120 × 20/3 = 800 litres.
Answer: 800 litres

Problem: {problem}
Reasoning:"""

problem = """A train and a car start from the same city at 08:00.
The train travels at 160 km/h; the car at 100 km/h.
How far apart are they at 10:30?"""

response = prompt(
    "You are a precise mathematics tutor.",
    FEW_SHOT_COT.format(problem=problem)
)
print(response)

  Travel time = 08:00 to 10:30 = 2.5 hours
  Train distance = 160 × 2.5 = 400 km
  Car distance  = 100 × 2.5 = 250 km
  Distance apart = 400 − 250 = 150 km
Answer: 150 km apart

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10.2.4. Step-Back Prompting

Step-back prompting (Zheng et al., 2023) asks the model to first retrieve the underlying principle or concept before solving the specific problem. This prevents the model from jumping to an answer without activating the relevant knowledge.

Pattern: “What general principle applies here? → Apply that principle → Answer.”

STEP_BACK_TEMPLATE = """Before answering the specific question, step back and identify
the underlying concept or principle. Then apply it to answer.

Question: {question}

Step 1 — What general concept or principle is relevant here?
Step 2 — Apply that principle to this specific case.
Step 3 — State the final answer clearly."""

questions = [
    "Why does mixing red and blue light give magenta, but mixing red and blue paint gives purple?",
    "A Python list and a Python tuple look similar — when should I prefer a tuple?"
]

for q in questions:
    print(f"Q: {q}\n")
    print(prompt("You are a clear and precise explainer.", STEP_BACK_TEMPLATE.format(question=q)))
    print("\n" + "─"*70 + "\n")

Q: Why does mixing red and blue light give magenta, but mixing red and blue paint give purple?

Step 1 — Relevant concept: additive vs subtractive colour mixing.
  Light uses additive mixing (RGB): combining red + blue adds wavelengths → magenta.
  Paint uses subtractive mixing (CMY): each pigment absorbs certain wavelengths;
  red paint absorbs cyan, blue paint absorbs yellow → together they absorb most
  wavelengths except a narrow band near purple/violet.

Step 2 — Application: the physical medium determines how colours combine.

Step 3 — Red + blue light → magenta; red + blue pigment → purple/violet.

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10.2.5. Self-Ask Prompting

Self-Ask (Press et al., 2022) trains the model to decompose a complex question into simpler sub-questions, answer each one, then synthesise the final answer. Particularly effective for multi-hop factual queries.

SELF_ASK_TEMPLATE = """Answer the question by first asking and answering relevant
sub-questions, then giving the final answer.

Format:
  Follow-up question: ...
  Intermediate answer: ...
  (repeat as needed)
  Final answer: ...

Question: {question}"""

question = "Was the president of France when the Eiffel Tower was built also the president when the first Tour de France took place?"

print(prompt(
    "You are a precise research assistant.",
    SELF_ASK_TEMPLATE.format(question=question)
))

Follow-up question: When was the Eiffel Tower built?
Intermediate answer: The Eiffel Tower was constructed between 1887 and 1889,
  completing in March 1889.

Follow-up question: Who was the president of France in 1889?
Intermediate answer: Sadi Carnot was President of France in 1889.

Follow-up question: When was the first Tour de France?
Intermediate answer: The first Tour de France took place in July 1903.

Follow-up question: Who was the president of France in 1903?
Intermediate answer: Émile Loubet was President of France in 1903.

Final answer: No. Sadi Carnot was president during the Eiffel Tower's construction
(1889), but he was assassinated in 1894. Émile Loubet was president during the
first Tour de France (1903).

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10.2.6. Contrastive Chain-of-Thought

Contrastive CoT provides both a correct and an incorrect reasoning trace in the few-shot examples — labelled explicitly. The model learns to distinguish good from poor reasoning, improving the quality of its own traces.

CONTRASTIVE_COT = """I will show you correct and incorrect reasoning, then ask you to solve a new problem correctly.

INCORRECT EXAMPLE:
Problem: If 5 workers build a wall in 10 days, how long for 2 workers?
Reasoning: Fewer workers → take less time. 5−2=3 fewer workers → 10−3=7 days.
Answer: 7 days ← WRONG (this reasoning is incorrect)

CORRECT EXAMPLE:
Problem: If 5 workers build a wall in 10 days, how long for 2 workers?
Reasoning: Total work = 5 workers × 10 days = 50 worker-days.
           With 2 workers: 50 worker-days ÷ 2 workers = 25 days.
Answer: 25 days ← CORRECT

Now solve this problem using correct reasoning:
Problem: {problem}"""

problem = "A pump fills a tank in 6 hours. A second pump fills it in 4 hours. How long do they take together?"

print(prompt("You are a precise maths tutor.", CONTRASTIVE_COT.format(problem=problem)))

Reasoning:
  Rate of pump 1 = 1/6 tank per hour
  Rate of pump 2 = 1/4 tank per hour
  Combined rate  = 1/6 + 1/4 = 2/12 + 3/12 = 5/12 tank per hour
  Time together  = 1 ÷ (5/12) = 12/5 = 2.4 hours = 2 hours 24 minutes
Answer: 2 hours and 24 minutes ← CORRECT

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10.2.7. Tabular Chain-of-Thought

Tabular CoT (Ye & Durrett, 2023) structures reasoning as a markdown table, enforcing clear intermediate steps and reducing errors in multi-step computations. Especially effective for problems involving multiple entities or comparisons.

TABULAR_COT_SYSTEM = """Solve problems by constructing a step-by-step reasoning table.
Format each step as | Step | Operation | Value |
End with a clear Final Answer line."""

problem = """Three freelancers bid for a project:
Alice: €80/hour, estimates 40 hours
Bob:   €65/hour, estimates 55 hours
Carol: €90/hour, estimates 32 hours
Who offers the lowest total cost?"""

print(prompt(TABULAR_COT_SYSTEM, problem))

| Step | Operation               | Value            |
|------|-------------------------|------------------|
| 1    | Alice total cost        | €80 × 40 = €3200 |
| 2    | Bob total cost          | €65 × 55 = €3575 |
| 3    | Carol total cost        | €90 × 32 = €2880 |
| 4    | Minimum cost            | €2880 (Carol)    |

Final Answer: Carol offers the lowest total cost at €2880.

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10.2.8. When to Use Each Technique

Technique	Best for	Key trigger
Zero-Shot CoT	Any reasoning task, quick wins	“Let’s think step by step”
Few-Shot CoT	Consistent output format needed	2–4 worked examples with traces
Step-Back	Factual / conceptual questions	“What principle applies?”
Self-Ask	Multi-hop factual queries	“Follow-up question: …”
Contrastive CoT	Improving reasoning quality	Show wrong + right traces
Tabular CoT	Numerical / comparative problems	Markdown table format