COMMUTER OVERFLIES FINAL APCH COURSE AND HAS CLOSE PROX WITH MLG. CTLR ISSUES GAR.

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MY CAPT AND I WERE CONDUCTING A FLT FROM PSP TO LAX ON JAN/SUN/94. IT WAS LATER IN THE AFTERNOON; HAZY AND FOGGY IN THE LAX AREA WITH THE VISIBILITY ABOUT 2 MI. MY DUTY DAY HAD BEGUN 10 HRS EARLIER AND THIS WAS OUR SECOND TO LAST LEG OF THE DAY. I WAS FATIGUED AND CONCERNED WITH BEING ON SCHEDULE. AFTER RECEIVING THE ATIS AT LAX; AND INSTRUCTIONS FROM LAX APCH CTL; THE CREW BEGAN TO PREPARE FOR THE ILS RWY 25L APCH AT LAX. I WAS THE PF. AFTER THE CAPT HAD BRIEFED THE APCH AND IDENTED OUR NAVAIDS (LOM ; LOC; AND VOR) WE WERE ON RADAR VECTORS TO INTERCEPT THE FINAL APCH COURSE FOR RWY 25L AT LAX. ATC CALLED TFC FOR US; A 737; WHO WAS TO LAND ON A PARALLEL RWY. WE CALLED TFC IN SIGHT AND PROCEEDED WITH VECTORS. AFTER SEVERAL HDG ASSIGNMENTS; ALT STEP-DOWNS; AND SPD CHANGES; I BECAME DISTRACTED BY THE NUMEROUS INSTRUCTIONS AND FLEW THE ACFT THROUGH THE FINAL APCH COURSE. AS I BEGAN TO TAKE CORRECTIVE ACTIONS; ATC CALLED AND CANCELED OUR APCH CLRNC. THEY VECTORED US AROUND FOR ANOTHER ATTEMPT AT THE ILS 25L AT LAX. THE SECOND APCH WAS UNEVENTFUL AND SUCCESSFULLY COMPLETED. JUST PRIOR TO BEING HANDED OFF TO LAX TWR; ATC INFORMED US TO CALL; 'THE LAX APCH SUPVR AT OUR CONVENIENCE;' AND GAVE US THE PHONE NUMBER. MY CAPT CALLED THE SUPVR ABOUT 10 MINS AFTER LNDG. THE SUPVR SIMPLY ASKED HIM WHY WE HAD FLOWN THROUGH THE LOC. THE CAPT MADE NOTE OF THE DISTRS AND INFORMED HIM OF OUR CORRECTIVE ACTION; AND OUR CANCELED APCH CLRNC. THE SUPVR MADE NOTE THAT WE HAD COME 'CLOSE' TO THE 737 ON THE PARALLEL COURSE; BUT DID NOT ELABORATE ON ANY DISTANCE RELATIVE TO WHAT 'CLOSE' MEANT LITERALLY. THE SUPVR INFORMED MY CAPT 'FOR THE CREW TO PAY CLOSER ATTN' IN THE COCKPIT; AND AS LONG AS THE ACFT FILED NO RPT OR COMPLAINT THAT 'THIS MATTER WAS OVER AS FAR AS HE WAS CONCERNED.' I FULLY REALIZE THAT MY BEING FATIGUED AND SOME BREAKDOWN IN COM WITH MY CAPT ARE THE REASONS FOR MY HAVING TO WRITE THIS RPT. MY CAPT AND I DISCUSSED THE MATTER AND MADE PLANS AS TO HOW WE WOULD BE MORE COORDINATED AND COMMUNICATIVE IN THE FUTURE.