The difference with something completely new at inference time, that was not in the training data, or not used by RL training, is that while it will be able to use it to some extent, it has not been taught via RL how to best use in a reasoning chain.
The problem is that LLMs don't really have the generic ability to reason, so they instead need to fake it by either:
1) Fine tuning on reasoning data (very specific)
2) RL training (more generalizable, especially for math/coding)
3) Prompting that encourages "keep on going" "tree of thoughts" exploration where they may discover a reasoning chain largely by luck
Demis Hassabis has talked about combining LLMs with search (cf systems like AlphaGo) which sounds like it might be useful for math research.
> also i think that it is reasoning exactly like us humans do. Indistinguishable
Yes, it is copying human reasoning so it will appear the same, but the difference is when you don't know what to do/try next - when you are trying to solve a problem that you have never solved before and don't know from experience what to try next. This is when having real/generic ability to reason, not just "reason from memory" matters. This is when things like human curiosity are useful : "I wonder what happens if I try this ..."