ACR X TCASII RA WITH Y ON PARALLEL RWY MADE MISSED APCH. NON ADHERENCE TO ATC CLRNC.

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ACR X CLRED FOR THE ILS 25L AT LAX. NIGHT VFR CONDITIONS. APCH ASKED US 3 TIMES IF WE SAW THE ARPT. OBVIOUSLY; THEY REALLY WANTED TO GIVE US A VISUAL APCH. WHEN WE FINALLY PICKED OUT THE RWY; AMIDST ALL THE LIGHTS; THEY IMMEDIATELY TOLD US TO SIDESTEP TO THE R SIDE RWY 25R AND THEY TOLD US THERE WAS ACFT Y IN OUR 8 O'CLOCK POS THAT WAS GOING TO LAND ON THE L SIDE. VERY SHORTLY THEREAFTER; WE RECEIVED A TA ON TCASII. THE ACFT WAS MOVING IN FROM BEHIND US. WE CONTINUED OUR APCH. SHORTLY AFTERWARD; WE RECEIVED AN RA TELLING US TO SLOW OUR DSCNT RATE. WE LEVELED OFF SO THAT THE WARNING (AURAL WARNING) STOPPED; BUT THE TCASII STILL SHOWED RED AND THE VSI INDICATOR WOULD NOT LET US DSND BECAUSE OF THE OTHER ACFT. THIS SCENARIO STARTED AT APPROX 10 MI OUT; AND BY ABOUT 4 MI OUT; THE TCASII GUARANTEED THAT WE WERE IN NO POS TO LAND. I TOLD THE TWR THAT WE HAD A TCASII ADVISORY AND THAT WE COULDN'T DSND WITH THAT ACFT THERE. THE APCH CTLR ASKED THE OTHER ACFT IF THEY HAD US IN SIGHT. THE OTHER SAID THAT THEY DID HAVE US IN SIGHT. THE PROB IS THAT WE COULD NOT SEE THE OTHER ACFT; AND MORE IMPORTANTLY; WE COULD NOT DSND AND IGNORE THE TCASII WARNING. COMPANY POLICY; FAA; AND COMMON SENSE DICTATE THAT AN RA SHOULD NOT BE IGNORED. I TOLD THE TWR WE WOULD HAVE TO GAR. I BELIEVE THAT WE MADE THE PROPER DECISIONS AND TOOK THE PROPER ACTIONS; CONSIDERING THE SIT.