If you think all they need to do is "just that" (try, verify, repeat as you say) then I think you're very, very mistaken.

There is no way for the LLM to bruteforce the search space any better than a human. What it can do better, tho, is to make connections between seemingly (for us) unconnected notions and join them, then verify if that's right.

Your view is not only wrong but also condescending in this day and age.