ARTCC DSNDED RPTR TOO LATE AND TURNED RPTR INTO OTHER TFC PROMPTING A TCASII RA.

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WE WERE FLYING FROM DTW-ATL AT FL330. AT SOME POINT WE WERE TAKEN DOWN TO FL310. LEVEL AT FL310; WE WERE CLRED TO DSND TO FL290. PROCEEDING 'DIRECT ROME' AND 'ROME 8' ARR INTO ATL. OUR RATE OF DSCNT WAS COMPANY'S STANDARD RATE OF 1000 FPM ABOVE FL290. NEXT CTR GAVE US A TURN TO 270 DEGS FOR TFC; FOLLOWED BY 'EXPEDITE TO FL290' AND EXPEDITE TO HDG 270 DEGS. NEXT COUPLE OF ITEMS OCCURRED AT ABOUT THE SAME TIME. AN ACFT CALLED THE CTR TO ADVISE THEM THAT THEY HAD TFC CONFLICT ON THEIR TCASII. THE FO WAS FLYING AND WHEN I HEARD ACR X CALL I IMMEDIATELY NOTICED HIM ON OUR TCASII; ABOUT 1 O'CLOCK POS WITH '00' FOR ALT SEPARATION. OUR TCASII WENT OFF AND GAVE US AN RA. AT THIS TIME I DISCONNECTED THE AUTOPLT AND MANUALLY FLEW OUT THE RA AND LEVELED OFF AT FL290. AUTOPLT WAS RE- ENGAGED AND THE ACFT WAS PASSED BACK TO THE FO. AS WE PASSED UNDER ACR X; THE FO SAID HE NOTICED OUR SEPARATION INDICATED 1500 FT FROM ACR X AND WE ESTIMATED THAT WE PASSED WITHIN 2 MI HORIZLY OF EACH OTHER. THE CTLR WAITED TOO LONG TO TAKE US DOWN AND WHEN HE FINALLY DID; HE DID NOT ASK US TO 'EXPEDITE' OR ADVISE US THAT IT WAS FOR TFC UNTIL IT WAS TOO LATE. WHAT MADE THE SIT EVEN WORSE WAS THAT BY TURNING US TO A HDG OF 270 DEGS; HE TURNED US RIGHT INTO OUR TFC.