For me the issue is that there are so many pieces, I can't hold them all in my head together.

But that period of stepping away seems to allow me to combine a few pieces and then treat that new piece as a single piece, so I'm able to hold much more. (Easily noticeable when coding same program over time).

I don't think I can consciously do that. It only happens if I study and consider the problem daily for at least 4-5 days, sometimes longer.