When trying to express the idea of "cogitate about" in a more varied and expressive way, one could turn to a number of synonyms. To "mull over" something would suggest a slow, thoughtful consideration, while "ponder" implies a more serious and philosophical meditation. "Contemplate" is another option, which conveys a sense of deeper reflection and introspection. To "ruminate" on a subject gives the impression of a sustained and deliberate thought process, while "brood" implies a more moody or troubled form of thinking. "Deliberate", "meditate", "reflect" and "introspect" are other synonyms to describe the process of "cogitate about".