There are several synonyms for the phrase "carries forward," which means to continue or advance a particular activity, task or plan. Some alternatives include "progresses," "moves ahead," "advances," "propels," and "proceeds." These synonyms all indicate that something is being deliberately continued or pushed forward. They can be used to describe a variety of situations, such as the advancement of a project at work, the continuation of a conversation or the development of a new hobby. Whatever the context, using synonyms for "carries forward" can help add variety to writing and make it more engaging for readers.