这是 be careful to do sth. 结构。〔主语〕I 〔谓语动词〕have to be 〔表语〕very careful 〔目的状语〕not to offend the boss, 〔定语从句〕who could fire me at any time.参考译文：我得格外小心不去得罪老板，他随时会把我辞退的。
