SMA PLT HAS NMAC WITH SECOND SMA DURING PREP FOR ENTERING PATTERN.

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I WAS COMING BACK FROM POU FROM THE N. THE OTHER PLANE (HIGH WING CESSNA; SEL) WAS COMING FROM THE S. ATC TOLD ME TO FLY S TO SOUTHERN STATE HWY AND THEN FOLLOW IT INTO THE ARPT (TO HEAD W PARALLEL TO THE HWY). (SOUTHERN STATE RUNS E/W JUST S OF FRG). ATC TOLD THE OTHER PLANE (COMING FROM S) TO ALSO FOLLOW SOUTHERN STATE IN. I ARRIVED AT SOUTHERN STATE FIRST AND THEN TURNED W; FOLLOWING THE HWY. I WAS ON THE N SIDE OF THE HWY. THE CESSNA WAS FASTER AND STARTED FLYING ON THE SOUTHERN SIDE OF THE HWY; DIRECTLY OPPOSITE OF ME. ATC REPEATEDLY ASKED BOTH PLANES WHETHER WE SAW EACH OTHER. I RESPONDED THAT I DID. THE CESSNA RESPONDED THAT HE DID NOT HAVE ME IN SIGHT (EVEN THOUGH WE WERE AT THE SAME EXACT ALT; AND EXACTLY PARALLEL TO EACH OTHER). WE WERE NOW APCHING THE POINT WHEN WE WOULD HAVE TO ENTER THE L DOWNWIND. SINCE I WAS CLOSER TO THE ARPT (WE WOULD TURN N TO ENTER; AND I WAS N OF THE CESSNA). I PLANNED TO TURN FIRST AND THE CESSNA WOULD FOLLOW ME. THE CESSNA THEN WAS SLIGHTLY AHEAD OF ME; BUT STILL PARALLEL AND ON THE OPPOSITE SIDE OF THE HWY. HE THEN TURNED N TO ENTER THE L DOWNWIND; AND AT THAT EXACT MOMENT; ATC TOLD ME TO FOLLOW HIM. I IMMEDIATELY CUT PWR AND TURNED HARD AND S TRYING TO CUT BEHIND HIM AND INSIDE OF HIS TURN. I DID SO AND LOST ABOUT 500 FT OF ALT. I THEN COMPLETED A L 360; CLBED BACK TO 1100 FT; FOLLOWED HIM AND LANDED SAFELY. I TURNED L BECAUSE ATL TOLD ME AT THAT EXACT TIME TO FOLLOW HIM; I WAS ALSO AFRAID THAT TURNING R; HE WOULD COLLIDE INTO ME. ATC SHOULD HAVE TOLD HIM TO DO A L 360 DEG TO GET BEHIND ME; OR TOLD ME TO DO R 360 DEGS TO GET BEHIND HIM (BEFORE IT GOT THIS FAR). I SHOULD HAVE REQUESTED A R 360 DEG EARLIER WHEN I REALIZED HE DIDN'T SEE ME. I JUST COULDN'T UNDERSTAND; BEING SO CLOSE; HOW HE COULDN'T HAVE SEEN ME. (SPECIALLY WHEN HE TURNED INTO ME).