A light aircraft pilot entering the pattern at L70; a non-towered airport; reported an NMAC with another light aircraft on downwind.

Narrative

I was flying with two passengers from ZZZ to Agua Dulce airport (L70) on a sightseeing/pleasure flight under part 91; using a rented Cessna 172. The passenger in the front seat was pilot-rated and familiar with the area. The passenger in the rear seat was not pilot-rated but is familiar with aviation and flying in small airplanes. I was following highway 14 from the southwest; and made radio calls 7nm and 4nm from the field. I decided to overfly the runway at midfield to enter a downwind for runway 22. While crossing midfield at 3700 ft MSL I made another radio call and joined the downwind leg. I then heard the first transmission that another aircraft was on final. I had been on the CTAF since being transferred by SOCAL roughly over Newhall Pass; so I was surprised because this was the first radio call I had received from another aircraft in the area. I transmitted that I did not have the other aircraft in sight and asked if the other aircraft saw me. As soon as I said this I saw a low-wing single-engine airplane coming across my nose from left to right; roughly 50 ft below me and 200 to 400 ft from my aircraft laterally. I banked away from the other aircraft; altered my downwind and then followed this aircraft in the pattern. The other aircraft stayed in the pattern; conducted two go-arounds; and departed the area. The other aircraft made sporadic radio calls.