Altering the prompt will certainly give a different output, though. Ok, maybe "think about this problem for a moment" is a weird prompt; I see how it actually doesn't make much sense.

However, including something along the lines of "think through the problem step-by-step" in the prompt really makes a difference, in my experience. The LLM will then, to a higher degree, include sections of "reasoning", thereby arriving at an output that's more correct or of higher quality.

This, to me, seems like a simple precursor to the way a model like the new o1 from OpenAI (partly) works; It "thinks" about the prompt behind the scenes, presenting only the resulting output and a hidden (by default) generated summary of the secret raw "thinking" to the user.

Of course, it's unnecessary - maybe even stupid - to include nonsense or smalltalk in LLM prompts (unless it has proven to actually enhance the output you want), but since (some) LLMs happen to be lazy by design, telling them what to do (like reasoning) can definitely make a great difference.