When LLM's come up with answers to questions that aren't directly exampled in the training data, that's not proof at all that it reasoned its way there — it can very much still be pattern matching without insight from the actual code execution of the answer generation.

If we were taking a walk and you asked me for an explanation for a mathematical concept I have not actually studied, I am fully capable of hazarding a casual guess based on the other topics I have studied within seconds. This is the default approach of an LLM, except with much greater breadth and recall of studied topics than I, as a human, have.

This would be very different than if we sat down at a library and I applied the various concepts and theorems I already knew to make inferences, built upon them, and then derived an understanding based on reasoning of the steps I took (often after backtracking from several reasoning dead ends) before providing the explanation.

If you ask an LLM to explain their reasoning, it's unclear whether it just guessed the explanation and reasoning too, or if that was actually the set of steps it took to get to the first answer they gave you. This is why LLMs are able to correct themselves after claiming strawberry has 2 rs, but when providing (guessing again) their explanations they make more "relevant" guesses.