B737 CREW OUT OF LAX CLBING THROUGH FL285 FOR FL310 ENCOUNTER OPPOSITE DIRECTION TFC AT FL290 REQUIRING AN EVASIVE ACTION MANEUVER.

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CLBING OUT OF LAX; WE WERE CLRED TO FL310. CLBING THROUGH FL290; WE WERE NOSE-TO-NOSE WITH ANOTHER B737 THAT WAS LEVEL AT FL290. I SAW THE TFC ON TCASII AT 15 MI RANGE; WE WERE NOSE-TO-NOSE AT FL290. WE WERE CLOSING VERY RAPIDLY. I CALLED ZLA 126.52 TO ASK ABOUT THE TFC. JUST AS I WAS ASKING ABOUT THE TFC; THE TCASII WENT OFF WITH AN RA 'CLB.' GREEN DOT UP ABOUT 1800 FPM TO 2000 FPM; WHICH WE DID. CTR SAID TO TURN L TO A HDG OF 250 DEGS. ALL OF THE ABOVE HAPPENED AT THE SAME TIME. WE WERE IMC AT THE TIME AND NEVER SAW THE OTHER JET. WE REALLY YANKED AND BANKED. ATC CAUSED THIS EVENT. TCASII WORKED AS ADVERTISED; CREW WORKED AS ADVERTISED. THIS ALL HAPPENED VERY; VERY FAST. SUPPLEMENTAL INFO FROM ACN 566902: TCASII RA; NMAC. CLBING THROUGH FL285 FOR FL310; ANOTHER ACFT POPPED UP ON TCASII AT SAME ALT. IMMEDIATELY GOT RA 'CLB; CLB.' CAPT VERIFIED MAX PWR; AND I STARTED TURN TOWARDS L. CTLR GAVE NEW HDG OF 250 DEGS (APPROX 40 DEGS OFF HDG). CAPT INQUIRED AS TO TFC. CTLR STATED THAT OTHER TFC HAD PENETRATED OUR AIRSPACE. REMAINDER OF FLT WAS UNEVENTFUL. THIS EVENT HAPPENED VERY QUICKLY. I BELIEVE WE WERE WITHIN 5 SECONDS OF A HEAD-ON. THE TCASII WORKED PERFECTLY. WE WERE WITHIN APPROX 4 MI HEAD-ON WITH THE ACFT.