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Advanced Reasoning & Deep Analysis

60+ prompts engineered to unlock o3's extended thinking capabilities. From complex multi-step reasoning to scientific analysis, legal research, and hard coding challenges — get results that standard models can't match.

Category: Advanced AI Reasoning Models

Complex Multi-Step Reasoning

Strategic Problem Decomposer

I need to solve this complex problem: [describe problem]

Before giving solutions, think through it step by step:
1. Break the problem into its core components
2. Identify all hidden assumptions
3. Map the dependencies between components
4. Identify where the most uncertainty lies
5. Now propose 3 distinct solution approaches with trade-offs
6. Recommend the best approach and explain why

Show your full reasoning chain, not just the conclusion.

Competing Hypotheses Analyzer

I have these competing explanations for [phenomenon or situation]:
A) [hypothesis 1]
B) [hypothesis 2]
C) [hypothesis 3]

For each hypothesis:
1. What evidence would strongly support it?
2. What evidence would decisively rule it out?
3. Assign a rough probability (with reasoning)

Then tell me: what single piece of evidence would most efficiently distinguish between them? What should I go look for?

Root Cause Investigator

This problem keeps occurring: [describe problem]
Observed symptoms: [list what you see]
What you've already tried: [list any fixes attempted]

Use the 5-Why method and Fishbone analysis to:
1. Trace the root cause chain (go at least 5 levels deep)
2. Identify whether this is a systems problem or a local problem
3. Distinguish root causes from contributing factors
4. Recommend a fix that addresses the actual root cause, not just symptoms

Mathematics & Scientific Reasoning

Proof Walkthrough Builder

Walk me through a complete proof of [mathematical theorem or result].

Structure it as:
1. State clearly what we are proving and why it matters
2. State all assumptions and definitions needed
3. Lay out the proof strategy before beginning
4. Execute each step with explicit justification
5. Highlight the key insight that makes the proof work
6. Note any common mistakes people make when attempting this proof

Scientific Paper Critique

Critically analyse this scientific claim or study finding: [paste claim or abstract]

Evaluate:
1. Is the methodology appropriate for the claim being made?
2. What are the main confounds or alternative explanations not addressed?
3. What is the effect size and is it practically significant?
4. How well does the sample represent the population?
5. What follow-up studies would strengthen or refute this?
6. On a scale of 1-10, how much should I update my beliefs based on this?

Estimation Framework Builder

Use Fermi estimation to answer: [question requiring quantitative estimation]

Show your full reasoning:
1. Break this into estimable sub-components
2. State your assumptions for each component
3. Calculate a rough estimate with error bounds
4. Sanity-check the answer from a different angle
5. Identify which assumption, if wrong, would most change the answer
6. Give a final range: plausible low, best estimate, plausible high

Deep Research & Analysis

Literature Synthesis Engine

Synthesise the current state of knowledge on: [topic or question]

Provide:
1. The mainstream consensus view (with confidence level)
2. The main dissenting or minority positions
3. Key open questions the field has not resolved
4. The strongest evidence on each side
5. Your assessment of where the evidence actually points
6. What a careful non-expert should conclude from this

Distinguish clearly between what is well-established vs. still debated.

Devil's Advocate Stress Test

I believe: [state your position or plan]

Play the most rigorous devil's advocate possible:
1. Build the strongest case against my position (steelman it)
2. Identify the 3 assumptions my position most depends on
3. Find real-world examples where similar reasoning failed
4. List what I would need to be true for my position to be wrong
5. Then tell me: what should I think about this position after this analysis?

Be genuinely critical, not just contrarian.

Policy Impact Analyzer

Analyse the likely impact of this policy or decision: [describe policy]

Consider:
1. First-order effects (immediate, direct consequences)
2. Second-order effects (likely responses and adaptations)
3. Third-order effects (systemic changes over time)
4. Who benefits and who is harmed (be specific)
5. Historical parallels — similar policies and their outcomes
6. What conditions would make this policy succeed or fail
7. Your overall assessment: good idea, bad idea, or context-dependent?

Hard Coding & Systems Design

Algorithm Design Challenger

Design the most efficient algorithm for this problem: [describe the problem]

I want you to:
1. State the problem formally (input, output, constraints)
2. Analyse the naive brute-force solution and its complexity
3. Identify the key insight that enables a better approach
4. Design an optimised solution step by step
5. Prove (or argue) its correctness
6. Analyse its time and space complexity
7. Identify edge cases and how the algorithm handles them
8. Write clean pseudocode or code in [language]

System Design Deep Dive

Design a scalable system for: [system description, e.g. a ride-sharing backend]

Scale: [expected users / requests per second / data volume]

Cover:
1. High-level architecture and component breakdown
2. Data models and database choices (with justification)
3. API design for core operations
4. How you handle scale (caching, sharding, queues)
5. Failure modes and how the system degrades gracefully
6. The 3 hardest engineering problems in this design
7. What I would do differently at 10x the scale

Bug Reasoning Tracer

I have a bug I cannot explain. Here is the code and observed behaviour:

Code: [paste code]
Expected behaviour: [describe]
Actual behaviour: [describe]
Steps to reproduce: [list steps]
Environment: [language, version, OS, dependencies]

Reason through this systematically:
1. What are all possible explanations for this behaviour?
2. What does each explanation predict we would see?
3. Which explanation best fits the evidence?
4. What is the most likely fix?
5. What test would confirm the fix worked?

Data & Statistical Analysis

Statistical Interpretation Guide

I have these statistical results: [paste results or describe them]

Help me interpret them correctly:
1. What do these numbers actually mean in plain language?
2. Is the result statistically significant? Is it practically significant?
3. What are the main threats to the validity of this analysis?
4. What conclusions am I justified in drawing — and what would be overreaching?
5. What would I need to run a more rigorous analysis?
6. How should I communicate this finding to a non-technical audience?

Data Anomaly Investigator

I've noticed this anomaly in my data: [describe what you see]
Dataset context: [what the data is, how it was collected]
Normal pattern: [what you usually see]
Anomalous pattern: [what changed]

Reason through potential explanations:
1. Data quality or collection issues (list specific possibilities)
2. Real-world events that could cause this change
3. Statistical noise vs. genuine signal — how to tell the difference
4. What additional data would help diagnose this
5. Recommended next steps

Causal vs Correlation Auditor

I want to make this causal claim: [state your claim]
Evidence I have: [describe your data or observations]

Challenge my causal reasoning:
1. Is this correlation or causation? How strong is the evidence?
2. List 5 plausible confounders I might not have considered
3. What does reverse causality look like in this case?
4. What would a proper causal study look like to test this?
5. What is the most defensible claim I can make given this evidence?

Frequently Asked Questions

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