If you understand how this all works it's really no surprise that reasoning post-factum is exactly as hallucinated as the answer itself and might have very little to do with it and it always has nothing to do with how the answer actually came to be.

The value of "thinking" before giving an answer is reserving a scratchpad for the model to write some intermediate information down. There isn't any actual reasoning even there. The model might use information that it writes there in completely obscure way (that has nothing to do what's verbally there) while generating the actual answer.