I think LLM's chain of thought is reasoning. When trained, LLM sees lot of examples like "All men are mortal. Socrates is a man." followed by "Therefore, Socrates is mortal.". This causes the transformer to learn rule "All A are B. C is A." is often followed by "Therefore, C is B." And so it can apply this logical rule, predictively. (I have converted the example from latent space to human language for clarity.)

Unfortunately, sometimes LLM also learns "All A are C. All B are C." is followed by "Therefore, A is B.", due to bad example in the training data. (More insidiously, it might learn this rule only in a special case.)

So it learns some logic rules but not consistently. This lack of consistency will cause it to fail on larger problems.

I think NNs (transformers) could be great in heuristic suggesting which valid logical rules (could be even modal or fuzzy logic) to apply in order to solve a certain formalized problem, but not so great at coming up with the logic rules themselves. They could also be great at transforming the original problem/question from human language into some formal logic, that would then be resolved using heuristic search.