I don't think intent is a verb. It is either a noun or adjective. In the sentence "She is intent on winning the election" the verb would be "is" and "intent" is an adjective that describes her.

Compare:

His program focused on dinosaurs. (verb) His program is focused on dinosaurs. (adjective describing his program).

You would never say "his program intented on dinosuars" because it's not a verb.