What is the meaning of 着て行く?


I came upon these questions in my textbook. Here is the dialogue:
私は学校にせいふくを着て行きますが、何を着て行きますか。Now, I might assume 着て行く is close to 着ている as it
still makes sense using the latter, but why is this verb used, assuming it
acts as one, instead of the former?

