Here is my favorite mental-model for problem solving (and my favorite analogy)
So I have this problem:
I love eating scramble eggs, I hate cleaning up the pan and have been trying over the years many different techniques to make sure the egg's doesn't stick to the pan. (No I don't want teflon thanks).
So I tried different oils, temperatures and techniques, all with the goal of getting those delicious eggs not to stick in my pot/pan afterwards.
Then one day it hit me, I'm solving the wrong problem. The problem to be solved is not "EGGS NOT STICKING TO PAN", it's "FINDING A BETTER WAY TO CLEAN" the pan !
And I have found it, it's using a different type of plastic-scrubber. It looks like steel-wool, but it's all plastic.
So whenever I'm stuck on a problem for too long, I try and model the problem as an "eggs-in-pan" problem statement.