head toward someone or something
1. Lit. to point at and move toward someone, something, or some place. Head toward Mary and don't stop to talk to anyone else. Sharon headed toward the parking lot, hoping to get home soon.
2. Fig. to be developing into something; to be moving toward a specific result. The problem will head toward a solution when you stop making the situation worse than it is. I believe that you are heading toward severe health problems if you don't stop smoking.