A fresh start
At a certain point I felt that I could not move forward anymore in my mind. I started sorting out everything that I had gathered, and I kept what I thought was necessary to solve the problem. This strategy turned out to be beneficial in several ways:
1. Identifying the core
I had gathered so many papers and information, and tried tidbits here and there, only to get more and more desperate about not finding the right way to tackle the problem. Weeding through all I had accumulated helped me to determine for every document if was going to continue with that approach, or if I could file it again. I identified which strategy I should follow while getting rid of the approaches that didn't seem to work for my case.
2. File, don't pile
There's no use in having piles and piles of random stuff on your desk. If you can't process it any time soon, it's better to plan a moment in the near future to tackle it, and meanwhile file it in a place where you can find it back easily when you have the time to work on it. If you can't imagine when you will have the time to do it, delegate it or (if you're a PhD student and you're the lowest creature in the academic food-chain) just thrash it - it can't be that important.
3. A fresh start
Having everything cleared out (and even cleaned off my desk and rearrange my decorations a bit) helped me to make the switch: from now on, I'll flesh out this method to the bone, and I'll work on it until I have results.
I'm glad to say that this approach seems to pay off for me - maybe it was about determining which method to choose and then taking that road and ending my doubts about which path to follow, maybe it was about making a mental switch and starting anew with a different approach. Maybe this approach can help you when you get stuck...
What strategies do you apply when you get stuck? I'd love to hear from you!