Ceapaim might be better understood as I think so (in response to a question) or "I think that" (offering your opinion).
"I think" in the phrase "I think, therefore I am" or the original "cogito ergo sum" means a more active "think" - like ponder or "ruminate". Déanaim smaoineamh is literally "I make an idea", and reflects the more active sense of "I think" than ceapaim gives.
I would say tá mé ag smaoineamh ..., but Ceapaim go bhfuil.....
The NEID suggests ceap, meas, síl for the transitive meaning of believing or having an opinion (passively thinking, if you like), versus smaoinigh and machnaigh for the intransive meaning of "reflecting", (actively thinking).
If it helps, you could think of ag smaoineamh as "idea-ing", which isn't a word in English, but gives a better sense of the difference between ceap and smaoinigh.