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Brainstorming is a powerful tool when attempting to solve problems. Brainstorming is the process of listing out a bunch of ideas for a problem before exploring any of them in greater depth. Each brainstorming entry should not just be a formula or technique on its own; rather, each brainstorming entry should make a note of how the technique should be used. Note that for some problems, you will use one brainstorm entry to start a problem and simplify it, and then some number of other ideas to finish the problem.
Creating a brainstorming list also increases your stamina for tackling a problem, because when one method fails, you have a platter of other ones to try. Without these extra ideas at your disposal, you are more likely to give up on a problem prematurely.
Approach brainstorming like an English essay prewrite. Outline a pathway that you think may work and see if it flows logically. Attempt a few iterations of a function or sequence to see it there's a significant pattern. Solving math problems, like writing, involves revisions or rather numerous attempts.