swing, question, adapt, fluctuate, waver, doubt, vacillate, change one's mind, revise, vary, flip-flop, shift (one's perspective), alter (one's view), adjust to (new information), modify (one's views), shilly-shally, lose one's convictions, distrust (one's perspective), warm to the idea

lap up, swallow, view, dub, credit, buy, bank on, declare, believe, trust, take a position, posit, subscribe to, buy into, consider (credible), rest assured, have faith in, cling to, hold to (an opinion), take as gospel, place confidence in

plumb, ruminate, question (one's assumptions/beliefs), allow time (for an opinion to form), absorb, reflect, mull over, turn something over in one's mind, deliberate, consider, contemplate, ponder, come around, muse, pore over, revisit, digest, meditate on, cogitate, look over/at, roll over in one's mind, shape (a perspective)