A PLT HAS TO TURN TO AVOID ANOTHER ACFT WHILE LNDG AT CPS.

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THE FLT DEPARTED FROM SET; ST CHARLES COUNTY ARPT; TO CPS; PARKS DOWNTOWN ARPT. THE FLT PROGRESSED NORMALLY AND AT 8 NM NW OF CPS; I CONTACTED TWR AND WAS TOLD TO PROCEED. I SOON BEGAN TO SEE TFC DEPARTING AND ARRIVING TO THE ARPT. AT THIS TIME I SAW TFC AT MY 1 O'CLOCK POS AND ABOUT 1 MI. THE TFC WAS AT A HIGHER ALT THAN ME AND SEEMED TO BE TRAVELING SLOWER. TWR CONTACTED ME AND TOLD ME TO FOLLOW BEHIND THE TFC. I REQUESTED THAT I BE ALLOWED TO PASS TO THE L OF THE TFC. TWR CLRED ME TO PASS PARALLEL THE TFC. A MOMENT LATER I WAS AHEAD OF THE TFC AND STILL AT A LOWER ALT. THE TFC BEGAN TO ACCELERATE AND BEGAN A SLOW TURN TO THE L. I MAINTAINED MY CURRENT HDG. AS THE TFC DSNDED AND ACCELERATED; I DETERMINED THAT THEY MUST NOT HAVE SEEN ME. I BEGAN RETARDING THE THROTTLE TO ALLOW THE TFC TO PASS. A MOMENT LATER THEY SEEMED TO MAKE A HARDER L BANK AND DSNDED INTO MY FLT PATH. I PUSHED THE YOKE FORWARD AND BEGAN A L BANK AND RETARDED THE THROTTLE. TWR TOLD THE TFC TO WIDEN TO THE R AND CLRED THEM TO LAND ON RWY 4. I LEVELED OFF AND ENTERED A L DOWNWIND FOR RWY 30L AND TWR CLRED ME TO LAND. PROBS: 1) I BELIEVE THERE WAS A MISCOM OF WHO WAS SUPPOSED TO BE IN FRONT AFTER I WAS CLRED TO PASS. I SHOULD HAVE REQUESTED CLARIFICATION ONCE I NOTICED THE TFC TURNING TOWARDS ME. 2) FROM MY PERSPECTIVE; THERE WAS A SITUATIONAL AWARENESS PROB WITH THE PLTS OF THE OTHER ACFT.