General Aviation pilot reported an NMAC as they approached the airport. Pilot took evasive action to avoid a conflict.

Narrative

I was piloting Aircraft X; getting ready to land in Torrance; CA. I made a call on the 121.95 freq (PV practice area/Long Beach practice area); indicating that I was going to head towards Point Fermin. As I was making my way toward Point Fermin; I switched over my frequency to 133.07 (Torrance TWR for 29R) and started talking with Torrance Tower to land. Unfortunately; Torrance TWR instructed me to contact 124.0 (Torrance TWR for 29L). When I tuned into 124.0; I noticed that there was an aircraft talking with TWR; so I waited for my turn to speak. As I was waiting; I also did not want to break into Torrance's delta airspace so I decided to circle Point Fermin; left turn. This is when the conflict arose. As I was waiting to talk with Torrance TWR; and in the middle of my turn; I saw traffic coming at around my 9-10 o'clock position. It was also at this time that the Traffic Advisory on my aircraft started to warn me. A glance at the Traffic Advisory indicated that the second plane (Aircraft Y) was about 100 feet below me. Immediately; I started to climb; and just a couple of seconds later; I saw Aircraft Y passing me below. It looked like we had 200-300 feet of vertical separation between us. When I landed at Torrance safely; I immediately started to view the track logs of the flight and went on the website to get a better picture of what happened and what could have been done differently to prevent it. When viewing the track log; one of the biggest things that could have caused the problem was the lack of communication on what I was doing and what Aircraft Y was doing. At this moment; I was tuned into 124.0 (Torrance Tower 29L freq); and not on the CTAF frequency for the practice area (121.95). Due to this; I could not hear the intentions of Aircraft Y and in retrospect; Aircraft Y did not know what I was doing. Now after the mental debrief of the situation; one of the things that could have prevented this was if I monitored the 121.95 frequency while on the 124.0 to wait for my turn to speak. Another thing I could have done was instead of saying 'heading towards Point Fermin'; I could have announced that I was 'circling Point Fermin' before switching the frequencies. As for the Aircraft Y; I was not in their position so I do not know what occurred during this time. On the website; I do not know if Aircraft Y even noticed we were on a collision course as their altitude remained relatively consistent (4200-4300 feet) both during and before the incident.