How does one practice mindfulness during thinking - e.g. thinking about how to solve a problem?

This question is in context of practicing mindfulness in one's day-to-day activities (e.g. walking, talking, washing dishes etc.), where one is supposed to be "aware of" / "observe" / "be mindful of" these activities. But how does one be "mindful" during thinking, since the very act of "observing" thinking would interrupt the thought process? And, say, if the thought process is about solving a specific problem, the very act of "being aware of /observing" the thoughts would result in one being unable to effectively solve that problem - when compared to not observing/ not being mindful about those thoughts. Or, be unable to solve it all. The same question for when reading something very interesting, or studying, where one is fully engrossed? Wouldn't being mindful about these activities interrupt the reading/study? New to mindfulness here. Apologies if the question sounds foolish, or irrelevant due to my misunderstanding of mindfulness. Thanks in advance.