I would actually love if it would just ask me simple questions (just yes/no) when its thinking about something i wasnt clear about and i could help it this way, its a bit sad seeing it write out the assumption and then take the wrong conclusion
You probably have the hardware to run the smallest distill, it runs even on my ancient laptop. It's not very smart but it still does the CoT and you can have fun editing it.
You can add that to the prompt. If you're running into those situation with vague assumption, ask it to provide either the answer or questions to provide any useful missing information.