TXWY EXCURSION IN A NIGHT OP BY LNDG TAXIING TFC.

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WHILE TAXIING FLT AFTER LNDG AT LAX; I ENTERED INTO A NON APPROVED SURFACE AFTER LNDG. THE FO FLEW THE APCH AND LNDG TO RWY 7R AT LAX AND AT LOW SPD I TOOK CTL TO BEGIN RWY TURNOFF AND TAXI TO GATE. THE ARPT HAD A LOT FOR WATER IN LOW FLYING AREAS AND IT WAS DARK. THIS WAS MY FIRST EVER LNDG ON THIS RWY. WE BRIEFED THE TURNOFF AT INTXN 28 SO THAT WE WOULD NOT MAKE A REVERSE TURN AT INTXN 32. WITH THE DARKNESS; WATER AND MY UNFAMILIARITY WITH LNDG IN THIS DIRECTION (WHILE THE FO HAD HIS HEAD DOWN SETTING HIS RADIO TO TALK TO THE COMPANY); I LOST MY SITUATIONAL AWARENESS AND TURNED INTO THE HARD SURFACED AREA E OF TXWY 28 N OR OF RWY 7L. I HAD THOUGHT THAT I WAS BTWN THE RWYS 7L AND 7R AND THAT THE NW TURN OF TXWY 28 WAS TXWY 32 NW OF TXWY 28 BTWN THE 2 RWYS. FORTUNATLEY; GND CTL TOLD ME TO STOP AND WE BECAME AWARE OF WHERE WE WERE. I WAS ABLE TO SAFELY COMPLETE A 180 DEG TURN AND RETURN TO TXWY 28 AND TAXI TO THE GATE. THERE WAS NO DAMAGE TO THE ACFT OR TXWY LIGHTS; JUST TO MY EGO. NEXT TIME I WILL MAKE SURE THAT WE ARE BOTH HEADS UP WHEN XING RWYS IN CASE WE EVER GET LOST AGAIN. SUPPLEMENTAL INFO FROM ACN 293371: I TRANSFERED CTL OF THE AIRPLANE AFTER USING RUDDER STEERING AND SAFELY ON TXWY 28. THE CAPT SAID 'OK' ALOUD TO THE CTLR'S DIRECTIONS AND I ASSUMED HE KNEW WHERE HE WAS. UPON XING RWY 7L I WAS COMPLETING MY AFTER LNDG CHKLIST AND WAS CALLING COMPANY TO VERIFY OUR GATE AS THERE IS FREQUENTLY A CHANGE. I TRIED TO GET THIS DONE PRIOR TO SWITCHING TO GND FREQ BECAUSE OF POSSIBLE ALLEYWAY 30 CONGESTION. AS I LOOKED DOWN TO SWITCH RADIOS AND TALK TO COMPANY WHILE STILL LISTENING TO TWR; I NOTICED THE CAPT WAS STARTING TO TAXI ONTO AN UNLIT PAVED AREA STRAIGHT AHEAD INSTEAD OF MAKING A HARD L ON THE REVERSE HIGH SPD TXWY 28. I SAID 'STOP' RATHER FORCEFULLY. MY DUTIES WERE VERY COMPACT (CHKLIST; TALKING/LISTENING TO TWR AND CALLING RAMP). POSSIBLE LACK OF TXWY SIGNS/ENBEDDED LIGHTS TO CONFIRM RTE. AS FOR ME; IN THE FUTURE; I WILL VERIFY OUR TAXI RTE WITH THE CAPT PRIOR TO MY OTHER DUTIES AND BACK UP THE CAPT AT ALL TIMES. BOTH OF US DID HAVE OUR 10-9 MAPS OUT AND BRIEFED OUR EXIT PLAN OFF THE RWY BUT NOT TO THE RAMP -- BETTER BRIEFING NEXT TIME!