Why is 又…又 structure used to connect verbs here?
又…又 can connect adjectives， verbs or nouns!

Here are some examples:

那小伙又脏又臭， 可傻笑时却露出暴雪一般的牙齿。（He is dirty and stinks, but his laugh gave us a glimpse of his snow-white teeth.)

那小伙又小又廋， 还以为是个姑娘。(He is small and skinny, we thought he is a girl.)

着几个月又是台风又是海啸， 像是世界末日。(These few month is full of hurricane and tsunami, as if it were the end of the world.)

他那又是核武器又是生化武器， 却说是为了杀蚂蚁。(He's got nuclear weapons and bio weapon at home and claims it is for killing ants.)

可怜的女神又施法术又耐心等待可是他终究执迷不悟直到她终于觉得他无可救药了。(Poor Goddess used her divine power and patiently waited to make him walk the righteous paths unsuccessfully, long has passed until she thinks that he can no longer be saved)

难过的他又打又叫直到筋疲力尽啦。(the sad young man cursed and fight until he is exhausted.)

Sorry, my translations might not be accurate, but we got examples of 又…又 used with verbs, nouns and adjectives.