The best description of my problem solving process is the Feynman algorithm, which is sometimes presented as a joke where the hidden subtext is “be smart”, but I disagree. The “algorithm” is a surprisingly lucid description of how thinking works in the context of hard problems where the answer can’t simply be looked up or trivially broken down, iterated upon in a bottom-up fashion, or approached with similar methods.
Feynman’s thinking algorithm is described like this: