어서 나가다

go out after or because of something

-어서 links two things and can mean either "and then" or "because", and both readings appear here: 일어서서 나가다 "stand up and walk out" is sequence, while 마음에 들지 않아서 나가고 싶다 "want to leave because you don't like it" is cause. 나가다 is leaving an enclosed place or a group — a cinema, a country, a company — not just walking. If you want pure sequence with no hint of a reason, -고 나가다 is the safer link.