The phrase "moves toward" refers to an action of approaching a destination or goal. Some synonyms for "moves toward" include "advances," "progresses," "proceeds," "approaches," "draws near," "heads," "marches," "nears," "presses on," "sets out," and "travels." These words convey a sense of purposeful movement, indicating that the subject is actively making progress towards a particular objective. Whether used in a literal or figurative sense, these synonyms suggest a sense of motivation and forward momentum that can be helpful in describing a range of actions and activities.