ACR TAXIED ONTO WRONG RWY AT MIA. UNAUTH RWY ENTRY.

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AFTER STARTING 1 ENG; WE REQUESTED TAXI CLRNC AND WERE INSTRUCTED BY GND TO TAXI TO RWY 9L. WHILE TAXIING OUT GND POINTED OUT ANOTHER AIRLINER ON AN ADJACENT TAXIWAY WHICH WE WERE TOLD WAS OUR SEQUENCE. WHILE APCHING THE RWYS WE STARTED THE SECOND ENG AND THE FO CONTACTED OPS ON THE #2 RADIO TO GET OUR WT AND BAL INFO. JUST AS THESE TASKS WERE COMPLETE TWR INSTRUCTED US TO MOVE TO THE R ON THE LARGE TAXI AREA SO THE SEQUENCE ACFT (THE ONE DEPARTING AHEAD OF US) COULD MOVE INTO POS ON RWY 12 FOR TKOF. DURING THE PERIOD LEADING UP TO OUR TKOF SEVERAL ACFT HAD DEPARTED ON RWY 12. AFTER OUR SEQUENCE ACFT DEPARTED WE WERE INSTRUCTED TO TAXI INTO POS AND HOLD. WE TAXIED ONTO RWY 12 THINKING THAT WAS OUR ASSIGNED RWY. WHEN WE WERE IN POS ON RWY 12; TWR INFORMED US OUR ASSIGNED RWY WAS 9L. HOWEVER; WE WERE THEN TOLD TO DEPART ON RWY 12 AND TURN TO A 90 DEG HDG WHICH WE DID. THE FO BELIEVES TWR'S CLRNC INTO POS AND HOLD DID NOT INCLUDE A RWY ASSIGNMENT. AFTER SEEING ALL THE PREVIOUS ACFT; INCLUDING THE ONE WE WERE TO FOLLOW TKOF ON 12; I SIMPLY GOT IT INTO MY HEAD WE WERE ALSO TO USE 12; AND FORGOT ABOUT THE ORIGINAL 9L ASSIGNMENT FROM GND. LESSON WHEN GND SPECIFIES A RWY AT THE FIRST TAXI CLRNC THINK ONLY OF THAT RWY UNTIL TWR OF GND ASSIGNS ANOTHER. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO. SAYS HE WATCHED AS ALL THE PREVIOUS ACFT TKOF ON RWY 12 AND GOT MINDSET THAT 12 WAS THE RWY HE SHOULD ALSO USE. SECOND ENG START OCCURRED AS THEY APCHED THE RUNUP PAD WHICH SERVES BOTH RWYS 12 AND 9L. FLC WAS BUSY BUT NOT OVERLOADED. RWY INCURSION DID NOT CAUSE ANY TFC CONFLICT.