Extrapolate from stories about Adderall: infinite willpower for doing the wrong thing. The character winds up spending a year perfecting building toothpick castles eg.

My quick ideas are something like going from vacillating between exploration and exploitation strategies into pursuing pure exploitation and missing out on exploration paths, and generally ending up in failure modes of Hofstadterian sphexishness, where you doggedly keep at the same behavior when it obviously isn't working right in the circumstances. Though you could also use the power to pursue deliberate exploration and thinking things through, so it's not quite that simple. Still, now there's the meta-problem of whether the thing you're trying to think through is the best thing to be thinking about. For a historical analogue, would this end up with you staying up for weeks cranking out the best machine code with 1950s computers while people without the superpower decide that cranking out machine code for weeks at an end is horrible and go ahead to invent Lisp and Fortran? If you resolve to do something that's too difficult, like proving whether P != NP, will you ever stop? How will you figure out the correct level to figure out things, so that you neither end up arranging pebbles instead of inventing a compiler nor end up trying to solve all of philosophy and never get anywhere because it's too hard for you? How do you end up deciding to turn the power off anyway once you've turned it on? I guess there could be a natural control there, like you eventually falling unconscious from lack of sleep and waking up with the power turned off. What if there isn't?