A scripted puzzle example comparing one path that does not revisit its opening with a tree that scores alternatives and backtracks. No model runs here.

A step can be judged before the answer exists

This scripted example compares one fixed reasoning path with an explicit search over alternatives. A language model can write corrections within one path; a search procedure also keeps separate branches to revisit.

Sure / maybe / hopeless are guesses about an unfinished state, and they are what makes the search possible. Grade only finished answers and you learn nothing until it is too late to steer.