AN ACR MLG CREW FAILED TO CLB WHEN CLRED. THIS CAUSED LTSS WITH AN ITINERANT ACFT.

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THE FO WAS HAND FLYING THE DEP FROM EWR. AT 2500 FT; HDG 280 DEGS; THE CTLR GAVE US A MULTI-PART CLRNC TO 'CLB TO 6000 FT; HDG 220 DEGS; AND INTERCEPT THE 350 DEG RADIAL OF COLTS NECK.' I SET THE 6000 FT IN THE MCP ALT WINDOW; 220 DEGS IN THE MCP HDG WINDOW. THE FO APPARENTLY DID NOT HEAR THE 'CLB TO 6000 FT' PART OF THE MULTI-PART CLRNC AND CONTINUED TO MAINTAIN 2500 FT. DURING THIS TIME TCASII ISSUED A TA. THE TFC WAS DISPLAYED ON THE HSI 1000 FT BELOW US. WHILE WE WERE STILL SETTING UP THE NAV SYS TO COMPLY WITH THE CLRNC; TCASII ISSUED AN AURAL RA TO 'REDUCE DSCNT' FOLLOWED CLOSELY BY 'MONITOR VERT SPD.' SINCE I WAS SETTING UP THE 'INTERCEPT LEG TO' COLTS NECK; I WAS NOT COMPLETELY IN THE AIRPLANES' VERT SITUATION LOOP AND THOUGHT WE WERE CLBING SINCE I DID NOT YET REALIZE THE FO HAD NOT HEARD THE CLRNC TO CLB. BECAUSE IN MY MIND WE WERE CLBING AND MY ATTN WAS DIVIDED BTWN TALKING TO THE CTLR AND SETTING UP THE NAV SYS; I MISTAKENLY INTERPRETED THE TCASII WARNING AS MEANING 'LEVEL OFF.' IN RESPONSE TO THE CTLR'S CLRNC TO CLB; I TOLD HIM WE WERE RECEIVING A TCASII RA WHICH INDICATED NOT TO CLB. AT THE SAME TIME; I WAS CHKING THE ADI FOR VERIFICATION OF THE AURAL WARNING. IT TOOK ME A FEW SECONDS TO CORRECTLY ANALYZE THE ADI AND REALIZE THE TFC WAS BELOW US. THE ADI SHOWED THE AIRPLANE SYMBOL ABOVE THE RED TRAPEZOID. AS SOON AS I CORRECTLY UNDERSTOOD THE SITUATION; I ADVISED THE CTLR WE COULD AND WOULD CLB AND URGED THE FO TO CLB TO 6000 FT. THE NEXT CTLR ADVISED ME THAT THE PREVIOUS CTLR WAS FILING A PLTDEV RPT. IN TALKING TO THE EWR TRACON MGR LATER FROM W PALM BEACH; I WAS TOLD THAT ATC IS OBLIGED TO FILE A DEV WHEN TCASII IS INVOKED FOR NOT FOLLOWING THE CTLR'S CLRNC. SHE ALSO INDICATED THE CLOSEST POINT OF APCH WAS APPROX 1.5 MI AND 700 FT. SUPPLEMENTAL INFO FROM ACN 222898: A CONTRIBUTING CAUSE MAY HAVE BEEN WE WERE CLRED INITIALLY NEWARK 4 DEP; AFTER TKOF WE WERE GIVEN A VECTOR TO INTERCEPT A RADIAL (AND MAYBE A CLB CLRNC I DIDN'T HEAR). WE WERE EXTREMELY BUSY WITH CONFIGN CHANGES AND RETUNING RADIOS. EVERY EFFORT TO COMPLY WITH CLRNC WAS PERFORMED. SIGNIFICANT DEVS TO INITIAL CLRNCS WHILE IN CRITICAL PHASE OF FLT WITH HIGH WORKLOAD AS WELL AS MULTIPLE DIRECTIVE CLRNC IS A RECIPE FOR TROUBLE. ALSO; NOTE IF A CLB CLRNC WAS ISSUED IN THE INITIAL MULTIPLE DIRECTIVE CLRNC. NO URGENCY IN THE CLRNC WAS INDICATED AS IS COMMON WITH POTENTIAL CONFLICTS.