-(으)려고 gives the purpose and 나오다 is coming out. Watch how wide 나오다 is here: leaving the house (바람을 쐬려고 나왔는데, 'I came out for some air'), appearing on a show (어떤 이야기를 하시려고 나오셨나요?), turning out to vote (투표하려고 나오겠냐?), and coming to the table (EU가 협상하려고 나왔을까?).