"If you’re making requests on a ChatGPT page and then pasting the resulting (broken) code into your editor, you’re not doing what the AI boosters are doing. No wonder you’re talking past each other."

This is in fact what I am doing (though I am not trying to convince anyone not to use LLMs). How can I get into this other mode? Any pointers? Do I need to pay up for a service? I do not want to carry out vibe coding, I want to use LLMs to solve physics, math and logic problems/puzzles. I'd appreciate any recommendations.