There are various synonyms for the phrase "took vengeance", each with their own unique nuance. Avenged, reprised, retaliated, and paid back all connote acts of getting even or exacting justice. Revenge, retaliate, punish, and requite all suggest a desire for retribution or retaliation towards someone who has wronged them. Get even, strike back, and give someone their comeuppance are also commonly used synonyms when the focus is on balancing the scales of justice. Whatever the synonym may be, the overall implication is the same: a sense of vindication and triumph after making someone pay for their indiscretions.