Consider a mid-level PhD student in a STEM field (maybe 2-3 years into the program), he and his advisor are working on something relatively new and interesting but they have reached a point where the research isn't moving ahead. How do you get out of this situation?
All papers have been read, colleagues have been consulted and top-of-the-head alternatives considered but the problem isn't moving ahead. No theory, computation or intuition helps. The only possibility left is to (optimistically) wait for a Hollywood moment when it all comes together.
Where do you go from here assuming that you cannot completely abandon that topic? At what point should you "start searching for other problems"? How do you choose what to work on next (should you start anew or pick something allied)?