At least in this scenario it cannot utilize CoT to enhance its non-aligned output, and most recent model improvements have been due to CoT... unclear how "smart" a llm can get without it, because they're the only way it can access persistent state.
Maybe there’s an angle there. Get a guess answer, then try to diffuse the reasoning. If it is too hard or the reasoning starts to look crappy, try again new guess. Maybe somehow train on what sort of guesses work out somehow, haha.