Why 'think step by step' works
Language models generate text one token at a time, and each new token is influenced by everything generated before it. That has a surprising consequence: if you ask a model to jump straight to a final answer on a multi-step problem, it commits to an answer before it has 'worked through' the reasoning, and errors compound. If you instead ask it to reason through the problem first and give the answer last, the reasoning tokens become part of the context that informs the final answer, which measurably improves accuracy on math, logic, and multi-step reasoning tasks.
This technique is called chain-of-thought prompting, and it's as simple as adding 'think step by step' or 'explain your reasoning before giving the final answer' to a prompt. Some newer models, like OpenAI's o-series or Claude with extended thinking, do a version of this internally by default, but for everyday prompting with standard models, explicitly asking for reasoning still makes a real difference on non-trivial tasks.