Cause, bring about (6)
(Other definitions for prompt that I've seen before include "Give cue to forgetful actor" , "Arriving on time" , "Cause; done at once" , "Bring about; on time" , "keeping to the right time" .)
(Other definitions for induce that I've seen before include "Persuade or bring on, say birth" , "Give rise to" , "Bring on, cause to happen" , "Persuade, hasten childbirth" , "Bring on by artificial means" .)