A C172 EXPERIENCED NMAC ON SHORT FINAL TO BFI WHEN ACFT BELOW IS ISSUED GAR BY ATC.

Narrative

WE WERE IN THE RWY 13L PATTERN FOR TOUCH AND GOS WHEN WE HAD A NEAR MIDAIR ON VERY SHORT FINAL. TWR ASKED ME IF I HAD MY TFC IN SIGHT AND I REPLIED; 'NO; I AM ON SHORT FINAL.' HE THEN TOLD THE OTHER AIRPLANE TO GO AROUND AT WHICH TIME THEY CAME UP FROM UNDER US AND THE NEAR MISS HAPPENED. WE MISSED BY ABOUT 10 FT. WE ROLLED INTO A STEEP RIGHT TURN AT ABOUT 150-200 FT AGL TO AVOID THEM. I DO NOT EXACTLY REMEMBER WHAT WAS TOLD TO US ON DOWNWIND; BUT I CAN GUARANTEE WE WERE NOT TOLD THAT WE WERE #3 ON APCH. AFTER WE LANDED; I TALKED TO THE OTHER PLT AND HE INFORMED ME THAT HE WAS TOLD TO EXTEND HIS DOWNWIND FOR ANOTHER AIRPLANE ON A LONG STRAIGHT IN. THIS HAPPENED WHILE I WAS ON THE UPWIND. I BELIEVE I WAS CLRED #2. OUR TWR HAS ALSO BEEN CONDUCTING TRAINING AND THAT WAS THE CASE TONIGHT. THERE WERE THREE OR FOUR INSTANCES WHERE THE SUPERVISOR WOULD GET ON THE RADIO AND CORRECT THE TRAINEE. THIS HAPPENED IN THE MOMENTS BEFORE THE NEAR MIDAIR. I FEEL THAT THERE WERE A QUITE FEW PEOPLE TO BLAME. ME AND MY STUDENT DID NOT SEE AND AVOID. THE TWR CTLR DID NOT TELL US ABOUT THE TFC; AND TO A LESSER DEGREE; THE OTHER PLANE DID NOT SEE AND AVOID. THERE WERE TWO PLTS IN THAT PLANE. ANY ONE OF THE SIX OF US (INCLUDING THE TWR SUPERVISOR) COULD HAVE PREVENTED THIS. THE FACT THAT IT HAPPENED AT NIGHT; IN LIGHT HAZE; AND WITH A TRAINING CTLR DOESN'T HELP THE SIT. NOT SURE WHAT TO SUGGEST OTHER THAN ALL SIX OF US DOING OUR JOB A BIT BETTER; ESPECIALLY ME.