Even in the mathematical/formal realm, the meaning of reasoning is not as clear as it seems. The result of the activity of reasoning may be a formal argument that can be evaluated according to well-defined rules, but the actual process your mind went through to get there is just as opaque (or more) as whatever is going on inside LLMs. It seems likely, as you suggest, that we are going to have to define reasoning in terms of ability to solve certain classes of problems but leaving the character of the process unspecified.