ACR HAS CONFUSION REF CLRNC TO DSND AND FREQUENT CHANGES AS DSNDING. CLRED FOR VISUAL WITH TA NO POS GIVEN. TCASII RA; EVASIVE ACTION.

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PRIOR TO THE ABOVE EVENT AN INCIDENT OCCURRED THAT HELPED LEAD UP TO THE RPTED EVENT. WE WERE CLRED (JUST PRIOR TO OUR NORMAL DSCNT POINT) BY LAX CTR TO CROSS 40 MI S OF VTU. WE ASSUMED THE CTLR MEANT 40 MI THE OTHER SIDE OF VTU (OR SE). BEFORE WE THOUGHT TO QUESTION THE INSTRUCTIONS WE HAD A CHANGED CLRNC TWICE. FIRST TO STOP AT FL350; THEN REVISED TO FL310. THEN A FINAL CLRNC TO NOW CROSS 30 S AT 220. BY THIS TIME WE WERE ONLY 40 MI FROM VTU AND I QUESTIONED WHERE THE CTLR WANTED US TO CROSS AND DISCOVERED HE WANTED US TO BE AT FL220 IN 10 MI. WE THEN TOLD HIM WE THOUGHT HE MEANT 30 MI THE OTHER SIDE OF VTU AND WOULD NOT BE ABLE TO MAKE THE XING RESTRICTION. THE CTLR INDICATED IT WAS NO PROBLEM; BUT WHEN WE SWITCHED OVER TO APCH HE GAVE US 5 HDG ADJUSTMENTS TO SEQUENCE US IN WITH TFC. THE ABOVE SCENARIO LEAD TO SOME CONFUSION ON OUR PART AS TO EXACTLY WHERE WE WERE. HE THEN TOLD US WE WERE ON DOWNWIND FOR RWY 24R AND DID WE HAVE THE RWY IN SIGHT. THE COPLT SAID HE DID AND I SAID TO LET THE CTLR KNOW. THE CTLR THEN SAID 'CLRED VISUAL TO 24R.' WE ACKNOWLEDGED AND HE SAID 'START TURN TO BASE; NOW.' WE WERE 2000 FT HIGH AT THAT POINT AND I WAS CONCERNED IT MIGHT BE A PROBLEM. I ALSO DID NOT KNOW EXACTLY WHERE THE RWY WAS BECAUSE IT WAS ON THE COPLTS SIDE. WE WERE NOW SWITCHED OVER TO TWR (AT THIS POINT WE WERE 5200 FT MSL AND 9.0 MI FROM RWY). I STILL DID NOT HAVE THE RWY VISUALLY. THE CTLR SAID TO WATCH FOR AN LTT AND DID NOT GIVE AN O'CLOCK POS. THE COPLT SAID; WE 'WERE LOOKING;' WHEN WE GOT A TA ON THE TCASII. THE COPLT BECAME CONCERNED ABOUT THE TFC AND DID NOT REALIZE WE WERE GOING PAST THE CTRLINE OF RWY 24 COMPLEX. TWR ADVISED TO WATCH FOR TFC ON THE PARALLEL 25 RWYS (WITH MUCH CONFUSION GOING ON IN THE COCKPIT). THE SO (AND THE TCASII) BOTH ADVISED TO DSND AND TURN; WHICH I DID IMMEDIATELY. A R TURN AND BANK IN EXCESS OF 30 DEG WAS MADE TO AVOID THE LTT. THE SO ESTIMATED WE CAME WITHIN 1/2 MI OF THE LTT. WE THEN ESTABLISHED OURSELVES ON FINAL FOR 24L AND MADE AN APCH AND LNDG ON 24L.