💡 Detailed Explanation
The correct choice is 'やって' (te-form of 'やる' - to do). The grammar pattern '〜てしまう' (te-form + shimau) indicates the complete completion of an action (to finish doing completely). Sentence translation: 'Because I have completely finished all my homework, I am going out to play now.' The other choices are: 'やれて' (potential te-form: being able to do), 'やらせて' (causative te-form: let/make do), and 'やらなくて' (negative te-form: without doing), which do not combine with 'しまった' to express the completion of an action.