I have a question about the sentence 늦게 보내서 미안해요. I know that it basically means 'Sorry for the late answer' but I'm not sure what's the role of '게' and '서' in the sentence. I think adding 게 to 늦 is kind of like adding "ly" to it like 행복하다 /행복하게 = happy/happily so it's kind of like 'Sorry for answering slowly' and I think 서 means 'for' in this case (like 'sorry for...'). Are these correct?