Yes this is an extremely well known result for exactly the reason you guessed. It's not just abcktracking, asking an LLM to present a conclusion and then justify is also an excellent way to provoke hallucination as the model con concts "any justification that plausibly justifies the words it's already said".

This is the actual reason why openai _invented_ reasoning models, to give them time/space to work out a solution, rather than having to magic a correct solution out of thin air from token 1.

It's less important now that all models do reasoning, but it's still almost always better to make the output come out last rather than first.