WHILE ACR FLC WAS DISTR BY COURSE DEV AND ATC INTERVENTION; THEY FAILED TO RECOGNIZE THAT THE AUTOPLT DID NOT LEVEL AT ASSIGNED ALT.

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DURING CLB TO FL230 WE WERE GIVEN A HDG OF 020 DEG DIRECT SEAL BEACH AND A FREQ CHANGE. WE ROLLED OUT ON HDG JUST W OF SEAL BEACH AND WERE QUESTIONED BY ATC IF WE WERE DIRECT SLI. FO REPLIED YES; THEN CTLR TOLD US IT WAS E OF US; I REPLIED WE WERE GIVEN THE INITIAL HDG (020 DEG THEN DIRECT) AND WE WERE IN THE TURN. WE CHANGED FREQS AND CHKED IN. WE RECEIVED A QUESTION ABOUT OUR ASSIGNED ALT; (WE BELIEVE IT WAS FL230 BUT WE WERE SLOWLY CLBING THROUGH FL245). CTLR THEN CLRED US TO FL290. NO FURTHER DISCUSSIONS OF ALT PROBS WITH THE CTLR. CAUSE OF PROB; I THOUGHT THE AUTOPLT WAS IN THE COMMAND MODE AND HAD LEVELED OFF WHILE I WAS TALKING WITH THE CTLR ABOUT THE SEAL BEACH VECTOR. ACTUALLY; ACFT WAS IN THE CTL WHEEL STEERING MODE AND WOULD NOT LEVEL BY ITSELF. ANOTHER FACTOR; FATIGUE. BOTH PLTS COMMUTED IN TO THE BASE TO BEGIN THE TRIP. THIS WAS THE LAST LEG OF 7 LEGS WITH A 11:05 HRS SCHEDULED DUTY DAY. AFTER 4 HRS OF COMMUTING; WE WERE SCHEDULED FOR 7:40 FLT TIME. THIS COMBINED; I KNOW I WAS NOT AT MY MOST ALERT MENTAL ABILITY AND REALIZE I WAS TIRED. CORRECTION; TRY NOT TO COMMUTE IN TO A LONG DAY OF FLYING. SUPPLEMENTAL INFO FROM ACN 314358: CLBING OUT OF LAX; WE WERE DISTRACTED BRIEFLY BY ATC WHILE CLBING TO FL230. THE CONFUSION WAS QUICKLY SORTED OUT; CONCERNING GOING DIRECT SEAL BEACH (WE WERE IN THE TURN). CAPT RESPONDED AND WE THEN SWITCHED FREQS AND I CHKED IN. WE FAILED TO LEVEL OFF AT FL230.