Flight Instructor reported a near miss while turning final approach. The Tower directed the Instructor's aircraft to go around to provide separation.

Narrative

I am a CFI and took one of my students up for some traffic pattern work at the CCR airport from XA:00-XC:00 on Day 0; in Aircraft X. We started out in closed traffic on Runway 19R before the winds switched and Tower switched us to right traffic for 32 Right. On our second lap around the 32R Runway; at approximately XB:10; we were advised to look for traffic who was cleared for left base 32L. On our right base turn; we noticed the airplane; and how it was really close and getting closer. We turned final early out of an abundance of caution as things happen with parallel runways; and when we did; the other airplane turned final also; but they were almost directly behind us; aligned with 32R. They had overshot the 32L final approach path by a long shot; were almost directly behind us; and gaining. I estimate they were no more than 200 feet above us vertically; no more than 500 feet behind us horizontally. I took control from my student and immediately started configuring for minimum drag to increase our airspeed and get away from the other plane; after which Tower instructed us to go around. I can't be sure but I believe the other plane; based on traffic reports shortly after we got back on the ground and color identifiers; was Aircraft Y.