Well, the approach of solving a corpus (advocated by GP) doesn't leave room for the possibility of asking a follow-up question so you can't train for it that way.

GPT-3 was trained on a massive text collection so it can even ask for clarifying questions if the prompt context allows for it. Why? Because there are plenty of such examples in the training data.

Sure, but this is based on something kind of like “whether someone would be likely to ask for clarification here”, not based on whether GPT3 needs clarification.

Though, I’m confident that it should be possible to make something which, when unsure, asks for clarification.

In fact, I believe something at least rather similar is already done in, uh, I think it is called “delegative reinforcement learning”, where an agent takes actions, but when it is highly uncertain, it can instead choose to have an expert (who is assumed to be competent at the task, or at least has a tolerably low risk of very bad outcomes) to step in instead.

(Or, wait, maybe delegative reinforcement learning is still just used theoretically? Not sure.)

It could list all possible solutions based on the response to the followup question it would have asked.