Decomposition

In short: Break into subproblems from easiest to hardest.

What is: Decompose the problem into subproblems ordered from easiest to hardest and solve them in sequence, where each answer feeds the next.

When to use: Reasoning with sequential dependency, step 3 needs step 2's result.

When to avoid: Problems that don't decompose naturally into dependent steps.

💡 Tip: Explicitly ask for each stage's output before moving on, so errors don't propagate silently.

In short: Explore several reasoning paths and discard the bad ones.

What is: Instead of one line, the model explores several reasoning branches in parallel, evaluates each, and abandons those that don't lead to a solution. Like a chess player weighing moves.

When to use: Problems with several plausible approaches where you must compare and backtrack, planning, puzzles, optimization.

When to avoid: Simple tasks, the token cost is much higher than CoT.

💡 Tip: Reserve it for problems where linear CoT fails. The cost only pays off when there really are multiple routes to explore.

In short: The model writes code; an interpreter does the math.

What is: Instead of computing mentally, the model writes code (usually Python) representing the reasoning, and the calculation is run by an interpreter. Eliminates arithmetic errors.

When to use: Math, logic and data manipulation where numeric precision is critical and you can run the code.

When to avoid: When there's no runtime to execute, or the task isn't numeric/algorithmic.

💡 Tip: Ask for the code separate from the explanation, so you can run it directly without parsing.

In short: Break the task into sub-tasks; or outline before detailing.

What is: DECOMP breaks the task and delegates each sub-task to a specialized "handler" (another call or tool). Skeleton-of-Thought first generates the answer's skeleton (the headings) and then expands each point.

When to use: DECOMP in modular pipelines; Skeleton in long answers where keeping coverage and structure matters.

When to avoid: Short, direct answers, the extra structure adds nothing.

💡 Tip: In Skeleton, review and adjust the skeleton before expanding, fixing structure is cheap; rewriting all the content is expensive.