AN ACR MLG RESPONDED TO A TCASII ALERT. ARTCC SUPPLEMENTED THE TCASII ALERT WITH A DSCNT CLRNC.

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LEVEL AT 10000 FT; ATC GAVE TA VFR TFC AT 10500 FT; 1 O'CLOCK; APPROX 8 NM. INITIATED L TURN WHEN TFC POPPED UP ON TCASII. WHEN TFC WAS AT 5 NM AND 400 FT ABOVE US ON TCASII; INITIATED DSCNT WITH TA ON TCASII. WHEN TFC WAS 300 FT ABOVE US AND 2 NM; TCASII GAVE RA TO DSND AND I INITIATED AN EVASIVE MANEUVER OF TURN AND DSCNT AT 4000 FPM. PASSING 9500 FT; TFC PASSED OVERHEAD AT 100-200 FT INDICATED BY RA. NEVER SAW THE TFC VISUALLY. PAX IN FIRST CLASS ON THE R SIDE OF THE ACFT WINDOW SEAT SAW AN ACFT PASS OVER US DIRECTLY LESS THAN 400 FT. I PERSONALLY THINK THE TFC PROBABLY SAW US AND INITIATED A DSCNT THINKING HE WAS ON COLLISION COURSE. HIS DSCNT COINCIDED WITH OURS. WHEN WE WERE PASSING 9500 FT; THE TCASII INDICATED HE WAS 200-100 FT ABOVE US BEFORE A CLR OF CONFLICT WAS ISSUED. WE HAD TO DEVIATE FROM OUR ASSIGNED ALT. CTR GAVE US CLRNC TO 9000 FT WHEN WE WERE PASSING 9500 FT; THE SAME TIME THE TFC PASSED OVERHEAD. THE ATC ADVISORY SAVED THE DAY BECAUSE I STARTED A TURN WITH THAT AND INITIATED A DSCNT WITH A TA. THE TA WAS GIVEN AFTER I ALREADY STARTED THE DSCNT. I DID MAKE AN EVASIVE MANEUVER WITH THE RA. IF IT WEREN'T FOR BOTH THE ATC ADVISORY AND TCASII WE PROBABLY WOULD HAVE COLLIDED.