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.

Humans are also notoriously bad at this, so we have plenty of evidence that this lack of consistency does indeed cause failures on larger problems.