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The "chain of thought" thing where you tell it to "think step by step" is a slightly different thing. That's a single forward pass, where it can only reason based on what it output earlier. But once you reply to it, and the interface feeds the whole conversation back to the LLM, it now can look at the entirety of its previous answer.

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When it does it step by step it can look at every step when it writes down its final answer after the steps. There is no extra magic that happens just because you write something in between.

Edit: To expand on that, a humans inner thought would have caught the mistake at that point and corrected it by writing more instead of ending the text. The LLM basically never does that unless you tell it to fix the answer.

Every mistake you don't catch as being wrong in your inner thoughts simply become a part of your subjective experience/existence until challenged again later, if not forever.

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