You need to define the goal in a way that you will trust the completion. If you are not sure how you yourself would verify that there are 41, then you are in trouble. Verification must be deterministic, or it's worthless.

What the large models do really well nowadays, is that they won't lie to you if your deterministic verification fails. If you tell an OpenAI or Anthropic model that they need to run a certain `grep` or search or whatever command to verify, then they will do it. I haven’t seen them lie about this for a year, and trust them in this.