Neural networks are universal function approximators, transformers are universal sequence to sequence approximators. Crucially, the sequences here are the stream tokens in an LLM. This means an LLM can do arbitrary language manipulation.
If the reasoning task requires something that can't be done using language manipulation in embeddings-space, it won't be able to do it.
Idk, maybe my mathematical intuition is wrong, but it seems obvious to me that if all you have is a function on a vector (representing a token stream), then the only transformations you can create are ones that can be expressed in that vector space. In other words, if you express a problem in a more complicated space (e.g. a visual problem, or an abstract algebra problem), you will not be able to solve it in the smaller token space, there's not enough information. You COULD first transform the vector into a different representation, perform the transformation there, and then encode back.
This step would have to be different for every reasoning problem, so the underlying transformation to solution space would have to be generic and move into one of N reasoning subsystems.
Also, if we hypothetically assume this limitation doesn't exist, we would still have the issue that a trained LLM represents a single such transformation function.
If we want generic reasoning skills, the approximated function would have to be different for every reasoning problem. Even if we use a subset of the vectors degrees of freedoms to express each type of reasoning, it would make any truly reasoning LLM computationally intractable, because the embeddings space would blow up.