I don't know what the solution AI is but it has to be found.
The problem is that you're looking for a kind of solution that doesn't exist. There probably isn't now any undergraduate math problem that AI can't do, and if there is, there soon won't be. Trying to find kinds of problems that students can do but AI can't is fruitless.
The only answer is to get students to understand why they really need to do the work themselves -- and it's the same reason that they need to learn integration by parts even though the CAS can do it far faster and more accurately -- because learning develops their minds. And, for the students who are unwilling to understand, test them on it in a context where they can't rely on AI: Pencil and paper tests in a room free of any sort of electronics.