C177R PLT AND FLT INSTRUCTOR DEV FROM THE MISSED APCH PROCS AND THE CTLR ASSISTS WITH A NEW CLRNC.

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I WAS ON AN INST INSTRUCTIONAL FLT IN MY PRIVATELY OWNED CESSNA CARDINAL RG. WE WERE PERFORMING A VOR 1 APCH INTO BTV. PART OF THE APCH CLRNC WAS INSTRUCTION TO FLY THE MISSED APCH AS PUBLISHED. THE FLT INSTRUCTOR AND MYSELF HAD PRACTICED THIS APCH MANY TIMES IN MY C150; BUT THIS WAS THE FIRST TIME WE HAD FLOWN THIS PARTICULAR APCH IN THE CARDINAL. ADDITIONALLY; THIS WAS THE FIRST TIME WE HAD FLOWN THIS APCH IN MVMC/IMC. THE FACTORS OF SPD AND CONDITIONS HAD US WORKING MORE AS A FLT CREW THAN AS AN INSTRUCTIONAL FLT. MY INSTRUCTOR AND I WERE SHARING RADIO TASKS WHILE I WAS HANDLING ALL OF THE FLYING. SHE HAD WRITTEN DOWN THE 'AS PUBLISHED' FOR THE MISSED APCH WHEN WE RECEIVED OUR APCH CLRNC. AT THE MISSED APCH POINT; I INITIATED A MISSED APCH BY ADDING PWR; RAISING FLAPS; PITCHING UP; AND TELLING THE TWR WE WERE GOING MISSED. I WAS INSTRUCTED BY THE TWR TO SWITCH TO DEP. I SWITCHED OVER TO DEP AND RPTED IN. MY INSTRUCTOR THEN BEGAN SAYING 'TURN; TURN; TURN' AND POINTING TO THE L SIDE OF THE ACFT. I WAS NOT CERTAIN WHY SHE WAS SAYING THIS; BUT I EXECUTED A STANDARD RATE L CLBING TURN. I ASSUMED AT THAT POINT THAT WE WERE GOING BACK TO THE VOR FOR THE FULL PROC APCH. I FELT THAT MY MEMORY WAS AT FAULT AS I DID NOT THINK TO STATE THAT WE WERE TOLD TO EXECUTE THE PUBLISHED MISSED APCH. DEP THEN QUERIED OUR HDG; AND AS I WAS RESPONDING; I FULLY REALIZED THE MISTAKE WE HAD MADE AND THEN I ASKED DEP IF WE SHOULD HAVE DONE THE PUBLISHED MISSED APCH. AT THAT POINT DEP GAVE US A HDG AND STARTED DIVERTING ANOTHER ACFT THAT WAS APCHING. THE DIVERSION WAS THEN COUNTERED WHEN DEP DETERMINED US NOT TO BE A FACTOR FOR THE OTHER ACFT.