RWY INCURSION BY ARRIVING ACR B737 WHEN FLC CROSSED THE RWY 25R HOLD LINE.

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I WAS CAPT ON FLT FROM DENVER TO LOS ANGELES ON A B737- 300. WE LANDED LAX ON RWY 25L. MY FO WAS FLYING PLT. I ASSUMED COMMAND (CTL) OF THE ACFT AFTER LNDG ON ROLLOUT. WE WERE A LITTLE TOO FAST TO TURN OFF ON TXWY M AS I CONTINUED DOWN TO TXWY N AND TURNED R ON A TXWY I HAD NEVER PREVIOUSLY USED BEFORE. AS WE WERE APPROACHING TXWY N TOWER CONFIRMED OUR USING TXWY N AND ADVISED US OF A B747 USING THE P TXWY OPPOSITE DIRECTION. AS WE TAXIED OFF RWY 25L ON TXWY N; I SWITCHED THE RADIO TO GND CTL (WHICH I ALREADY PRESET) AND TOLD MY FO 'WE WERE ON GND.' HE WAS BUSY DOING HIS AFTER LNDG SOPS AND WAS SITUATIONALLY UNAWARE OF WHAT WAS HAPPENING OUTSIDE THE ACFT. I LOOKED TO MY L AT THE CARGO B747 ON TXWY P. THAT WAS WHEN I LOST SITUATIONAL AWARENESS BECAUSE I WASN'T LOOKING FORWARD WHERE MY ACFT WAS TAXIING. JUST A FEW SECONDS LATER BOTH OF US (MY FO AND I) REGAINED SITUATIONAL AWARENESS AND REALIZED WE WERE APPROACHING THE EDGE OF RWY 25R. I STOPPED THE ACFT AND OUR NOSE GEAR WAS ON THE WHITE RWY EDGE LINE WITH THE NOSE OF OUR ACFT PROTRUDING OVER. WE LOOKED DOWN THE RWY AND SAW AN ACFT QUITE A WAYS DOWN AS MY FO TOLD GND CTL WE WERE ON RWY 25R. FORTUNATELY TWR WAS WATCHING US APPROACH RWY 25R AND TOLD THE ACFT ON RWY 25R TO CANCEL TKOF CLRNC. GND CTL THEN TOLD US TO PROCEED ACROSS. I ELECTED TO STAY WHERE I WAS ON THE RWY EDGE AND NOT PROCEED ACROSS WHEN WE FIRST REALIZED WE WERE ON THE DEP RWY BECAUSE I KNEW THERE WOULD BE CLRNC FOR ANOTHER ACFT WHO MIGHT BE TAKING OFF LIKE THE ONE WE SAW WELL DOWN THE RWY HEADED TOWARDS US. THE THREE FACTORS WHICH CAUSED ME TO LOSE MY SITUATIONAL AWARENESS ARE 1) TURNING OFF ON A 90 DEGREE TXWY WHICH I DON'T RECALL EVER USING. 2) B747 DISTRACTION ON PARALLEL TXWY. 3) TWR DID NOT INSTRUCT US TO HOLD SHORT OF RWY 25R AND STAY WITH HER AS I AM USED TO HEARING. I COULD HAVE THOUGHT I LANDED ON RWY 25R AND SWITCHED TO GND AS I CLRED THE RWY. WHAT WOULD HAVE HELPED PREVENT THIS INCURSION WOULD HAVE BEEN TWR INSTRUCTIONS TO HOLD SHORT OF RWY 25R WITH THE REQUIRED ACKNOWLEDGEMENT ON OUR PART.