> It does not imply it either.

Right, it's irrelevant to the question of whether they can reason.

> to claim reasoning you need evidence

Frankly I have no idea what most people are talking about when they use the term and say these models can't do it. It seems to be a similarly hand-wavey exercise as when people talk about thinking or understanding.

> it needs to reliably NOT hallucinate results for simple conversations for example (if it has basic reasoning).

That's not something I commonly see in frontier models.

Again this doesn't seem related to reasoning. What we call hallucinations would be seen in something that could reason but had a fallible memory. I remember things incorrectly and I can reason.

> it does not actually take your code and debug it

It talks through the code (which it has not seen) and process step by step, can choose to add logging, run it, go through the logs, change what it thinks is happening and repeat. It can do this until it explains what is happening, creates test cases to show the problem and what triggers it, fixes it and shows the tests pass.

If that's not debugging the code I really don't know what to call it.