Reasoning models reason well, until they don't

I find that they know what they know fairly well, but if you move beyond that, into what can be reasoned from what they know, they have a profound lack of ability to do that. They are good at repeating their training data, not thinking about it.

The problem, I find, is that they then don't stop, or say they don't know (unless explicitly prompted to do so) they just make stuff up and express it with just as much confidence.

Every token in a response has an element of randomness to it. This means they’re non-deterministic. Even if you set up something within their training data there is some chance that you could get a nonsense, opposite, and/or dangerous result. The chance of that may be low because of things being set up for it to review its result, but there is no way to make a non-deterministic answer fully bound to solving or reasoning anything assuredly, given enough iterations. It is designed to be imperfect.