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

appraise, heed, examine, regard, mull over, assess, deliberate, consider, contemplate, evaluate, ponder, reflect on, take into account, respect, take into consideration, think (over/about), bear in mind, mind, note, check out/into, ruminate on, meditate on, chew over, look into/at

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)