> I simply cannot come up with tasks the LLMs can't do, when running in agent mode, with a feedback loop available to them. Giving a clear goal, and giving the agent a way to measure it's progress towards that goal is incredibly powerful.

It's really easy to come up with plenty of algorithmic tasks that they can't do.

Like: implement an algorithm / data structure that takes a sequence of priority queue instructions (insert element, delete smallest element) in the comparison model, and return the elements that would be left in the priority queue at the end.

This is trivial to do in O(n log n). The challenge is doing this in linear time, or proving that it's not possible.

(Spoiler: it's possible, but it's far from trivial.)