The phrase "rush in" means to act impulsively without thinking things through. If you want to express this idea in a more sophisticated way, there are many other phrases you can use as synonyms. Some of these include "act hastily," "make a rash decision," "jump the gun," "act recklessly," "be impetuous," "be imprudent," "be precipitous," and "be impulsive." These phrases can help you communicate the same basic idea in different ways depending on the context of your communication. So if you want to avoid using the same phrase repeatedly, consider using some of these synonyms instead.