That's different. You are pulling the model, semantically, closer to the problem domain you want it to attack.

That's very different from "think deeper". I'm just curious about this case in specific :)

I don't know about some of those "incantations", but it's pretty clear that an LLM can respond to "generate twenty sentences" vs. "generate one word". That means you can indeed coax it into more verbosity ("in great detail"), and that can help align the output by having more relevant context (inserting irrelevant context or something entirely improbable into LLM output and forcing it to continue from there makes it clear how detrimental that can be).

Of course, that doesn't mean it'll definitely be better, but if you're making an LLM chain it seems prudent to preserve whatever info you can at each step.