The bland verb think (from the Old English word thencan, and cognate with thank) is easily supplanted by any one of an impressive assortment of synonyms, each of which has a precise connotation think cannot match. Here are some to think about.
To cogitate is to think deeply and intently; the root of the word, which is unrelated to cognition (which refers to knowledge rather than thinking), stems from agitare (meaning “drive”), from which we also get agitate.
Contemplate connotes thought that is extensive as well as deep; another sense is “view as possible or probable.” The root of contemplatus, the Latin source word, is templum, the word for a place where omens are observed; it is cognate with temple.
Deliberate means to think carefully, as implied by its source, the adjective deliberate. An additional sense is “discuss before making a decision,” as when a legislative body meets to decide about whether to pass a law. (The derivation is from deliberare, meaning “consider carefully,” the root is possibly libra, meaning “pound” or “scale,” with the sense of weighing.)
To meditate is to focus one’s thoughts on something; the word, which can, alternatively, allude to planning, also refers to a mental exercise conducted in order to achieve a high state of spiritual awareness. (Meditate is derived from the Latin verb mederi, meaning “remedy,” and is related to medical and medicine.)
Mull, from the Middle English noun mul, meaning “dust,” is cognate with meal and refers not only to lengthy consideration but also to grinding.
Ponder has the connotation of carefully weighing a problem (as a matter of fact, ponder stems from the Latin verb ponderare, meaning “weigh,” and is related to ponderous), with the implication of extended inconclusive thinking. A similar term with the same etymological origin is perpend.
Reflect means, among other things, “think calmly and quietly”; its root is from flectere (meaning “bend”), which is also the source of flex.
To ruminate is to slowly and repeatedly go over something as if chewing it like a ruminant, a type of animal, such as a cow, that chews its food over and over again. (The word stems from the Latin term rumen, the name in that language and in English for part of a cow’s stomach.) “Chew over” is an informal synonym. Others include the word eye and the phrases “kick around,” “pore over,” and “wrestle with.”