Turn up reasoning effort for a genuinely hard analytical problem

Why this works

Claude's extended thinking mode allocates a separate reasoning budget the model uses to work through a problem before composing its final answer, and that budget is spent more effectively when the prompt gives it concrete work to do rather than leaving it to reason in the abstract — explicitly asking for an alternative approach to be considered and rejected, and for the final answer to be checked against the stated constraints before being presented, converts open-ended thinking into a checklist the reasoning trace has to satisfy. Naming this a multi-step reasoning task rather than a fast intuitive answer matters because Claude, like most models, allocates less internal deliberation to a prompt that reads like a quick factual question, so signaling task difficulty up front is itself part of getting the reasoning depth the problem needs. The self-verification step — check the final answer against the constraints, revise if it fails — is the single highest-leverage line in the prompt for optimization-style problems specifically, because these are exactly the class of problem where a fluent-sounding answer can silently violate a stated constraint (like exceeding a warehouse capacity) without the arithmetic looking obviously wrong on the surface. Asking for flagged assumptions closes the gap between a problem statement that is almost but not fully specified and an answer that quietly resolved the ambiguity one particular way without telling you it made a choice.