Is て form ever used before と思います

I just finished one of my finals and I realized I didn’t use short form of 起きるbefore と思います. I do have another attempt as it is an online final but timed and I would rather not take again as the last attempt is the one that’s submitted, not the best score. I think this is the only mistake I made but is it completely wrong? I guess I am asking if I should take again (I’m kinda a perfectionist) or if this still is a way to say it?
Context:
Question (although it doesn’t really matter): あした、何時におきなければいけませんか。
My answer was : 明日はテストがありますから早く起きなければいけません。六時半におきてと思います。

Any helpful reply is appreciated