There may be additional feedback loops, but fundamentally, that is what it is doing. Sure, it will show you what steps it takes to arrive at a conclusion, but it is just predicting the steps, the conclusion and the potential validity of the aforementioned based on its training data, not actually evaluating the logic or the truthiness of the output.
If you don’t believe me, ask your ”reasoning” LLM this question: What’s the name of the paternal great-great-grandfather of the son of Jacob’s son’s son’s son?