Well, "these kinds of approaches" isn't really a binary thing. When you're looking at a problem, you try a big mix of lots of different approaches - maybe you t

Well, "these kinds of approaches" isn't really a binary thing. When you're looking at a problem, you try a big mix of lots of different approaches - maybe you try making the problem smaller, and you get something that you could possibly crack if you made this extra assumption, and then your friend talks about their own unrelated work and you think "hold on, there's a bit of an analogy there", and you go back to your books and discover that a handy missing piece is actually Lemma 3.6 of some famous text, and you take a lot of showers, and eventually maybe the walnut shell has softened enough that you can peel a bit of it off.