My question involves a traffic accident in the State of: California

I got into an accident today backing out of a space in a library parking lot. I heard a honk and stopped, turned to look and saw another car waiting in the lane, I thought they were honking to let me know they were there. Apparently, the honk was a warning to what actually happened. I continued backing out until the collision in the middle of the lane. Another car was backing out of the space directly behind me. I pulled forward and got out of my car. The damage on their car was slight denting on the rear of their right quarter panel. My damage was on my passenger side bumper, pushed in. When I got out of the car the other party told me that they had stopped moving when they saw me and started honking. I did not hear this honking, only the honk from the other car. They did not want to get insurance or police involved, and we only exchanged phone numbers and drivers license information. We stated that we would discuss our options further after I had a chance to talk with my parents.

My question for you is what is the best way to proceed? Is this a case of 50/50 or some proportion? I never admitted fault but the way the conversation progressed it sounded like it was expected that I was at fault. Thank you for you're input.