is a predicate. と is used like a quotation particle.
So it's like:
as for this person, they said this.
Sue said she likes cats.
As for sue, she said she likes cats.
Same goes for と思います。
As for sue, I think she likes the cat.
I'm not good at explaining because I just learnt this myself but search up what a "predicate" is and it will help you understand a little more. I hope it helped a little. You can find this in chapter 8 of the Genki textbook if you have it. Send me a message and I will send you the information I have on this subject. :)