The reasoning generally isn't kept in the context, so after choosing the secret word in the first reasoning block, the LLM will have completely forgotten it in the second and subsequent requests.
So, it technically didn't change the secret word so much as it was trying to infer what its own secret word might have been, based on your guesses.
So, it technically didn't change the secret word so much as it was trying to infer what its own secret word might have been, based on your guesses.