There are various synonyms for the phrase "advance gradually." One such synonym is "proceed slowly." Another synonym is "move steadily." Other possible synonyms include "ease forward," "progress gradually," "creep ahead," and "inch forward." These synonyms all convey the same sense of moving forward slowly and steadily. In certain contexts, other synonyms may be more appropriate. For example, in the context of military maneuvers, the phrase "advance methodically" may be preferred. In any case, it is important to choose the synonym that best conveys the intended meaning and tone of the sentence or phrase.