TCASII AVOIDS A COLLISION BUT CAUSES NAV ERROR WHEN CREW DISTRACTED.

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I WAS TRACKING OUTBOUND ON THE FIM 136 DEG RADIAL AND DSNDING TO 7000 FT WHEN BUR APCH ISSUED A 130 DEG VECTOR TO JOIN THE BUR RWY 8 LOC AND FURTHER DSCNT TO 5000 FT. I WOULD ESTIMATE WE WERE ABOUT 4-5 MI FROM THE LOC CTRLINE WHEN THIS CLRNC WAS RECEIVED. THE ASSIGNED HDG AND ALT WERE SET ON THE FLT GUIDANCE PANEL AND I WAS IN THE PROCESS OF TUNING THE RWY 8 LOC WHEN WE RECEIVED A TCASII ALERT. I LOOKED AT THE TCASII SCREEN TO DETERMINE THE ORIENTATION OF THE TFC (APPROX 11 O'CLOCK AND 2 1/2 MI) AND THEN LOOKED OUTSIDE TO ACQUIRE IT. IMMEDIATELY THEREAFTER; AN AURAL TCASII RA 'MONITOR VERT SPD' SOUNDED WHICH BROUGHT MY ATTN BACK INSIDE TO THE VSI. AS THE AUTOPLT INITIATED ALT CAPTURE AT 5000 FT WE SPOTTED THE SMA PASSING L TO R UNDERNEATH US AT AROUND 4500 FT. AT THAT TIME BURBANK APCH ADVISED US THAT WE HAD OVERSHOT THE LOC COURSE. DUE TO THE DISTR OF THE TCASII WARNING I HAD FAILED TO ARM THE AUTOPLT TO CAPTURE THE LOC. AFTER THE XMISSION BY BUR APCH; THE TCASII AURAL 'CLR OF CONFLICT' SOUNDED. VECTORS WERE RECEIVED TO REJOIN THE LOC COURSE AND THE REMAINDER OF THE APCH AND LNDG WAS UNEVENTFUL. I DON'T BELIEVE MY ACTIONS CAUSED A LOSS OF SEPARATION WITH ANY ACFT.