Eviction help in Colorado

Original lease from 12/2020-12/2021, no issues, she was fired in 12/2021 and then the lies and games started. I decided to move back into my rental and on 04/06 I sent her an email (55 day notice) and outlined rent for April/May 2022, she paid April and now isn't paying and isn't leaving, she's a holdover tenant. It's my understanding in Colorado per JDF 97 paragraph #4, "no notice to quit shall be necessary from or to a tenant whose term is, by agreement, to end at a certain time." Per my notice of 04/06 - I believe I fall under this, is that correct, I do not need to give her notice? If that is correct, what is my next step, if it is not correct, what is my next step?