ACR X NON ADHERENCE TO ATC CLRNC FAILED TO MAKE TURN ONTO AIRWAY BECAUSE OF TCASII TA HAD CONFLICT WITH SMA Y. TCASII RA NOT COMPLIED WITH BECAUSE OF SEE AND AVOID CONCEPT.

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LEVELING AT ASSIGNED ALT OF 5000 FT; OBSERVED VFR ACFT AT 4500 FT LESS THAN 5 MI AT OUR 2 O'CLOCK POS ON TCASII DISPLAY. ACR X WAS ON ASSIGNED HDG OF 030 DEG TO INTERCEPT THE SAT 081 DEG RADIAL. UPON INTERCEPTION OF THE 081 DEG RADIAL WE OBSERVED THE VFR ACFT AT OUR 3 O'CLOCK POS CLBING AT 4700. RANGE LESS THAN 2 1/2 MI. ATC HAD NOT ADVISED US OF THIS ACFT. AS THIS ACFT WAS CLBING UP THROUGH OUR ASSIGNED ALT ON THE 081 DEG RADIAL (AIRWAY) THAT WE WERE TO MAKE A R TURN ONTO; I ELECTED TO MAINTAIN OUR CURRENT PARALLEL COURSE UNTIL THE VFR ACFT WAS ABOVE OUR ALT. THIS TOOK ACR X ACROSS THE CENTERLINE OF THE AIRWAY AND PROBABLY CLOSE TO THE NORTHERN EDGE OF THE AIRWAY SPACE BEFORE I OBSERVED THAT THE VFR ACFT WAS AT 5200 AND CLBING. AT THIS TIME I STARTED THE R TURN ONTO THE AIRWAY AND WE WERE ABLE TO OBTAIN VISUAL CONTACT ON THE ACFT. THE ACFT WAS 200 FT ABOVE AND LESS THAN A MI FROM ACR X AT THE 1 O'CLOCK POS. WE INCREASED OUR RATE OF TURN AND WAS ABLE TO PASS SAFELY BEHIND THE VFR TFC. THE TCASII SYS DID ISSUE AN RA DSND COMMAND DURING OUR TURN. HOWEVER; AS WE COULD SAFELY VISUALLY PASS BEHIND THE SMA; WE REMAINED AT THE ASSIGNED ALT. WE LATER WERE TOLD THIS WAS A VFR SMA KNOWN TO THE CTLR. I WOULD HAVE LIKED TO HAVE BEEN ADVISED OF THIS ACFT AND HIS INTENTIONS TO CLB THROUGH OUR ALT. FURTHER; I FELT THAT TO TURN MY ACFT AT A TARGET SHOWN ON THE TCASII DISPLAY LESS THAN 3 MI RANGE AT OUR ALT WAS UNSAFE AND A POSSIBLE COLLISION COURSE. HAD THE SMA REMAINED AT 4500 VFR AND NOT CLBING THROUGH OUR ALT ON OUR ASSIGNED COURSE; THIS WOULD HAVE BEEN AVERTED. THE CTLR NEEDED TO USE MORE DILIGENT SEPARATION AND ADVISORIES OF VFR TFC. SUPPLEMENTAL INFO FROM ACN 190228: TAKING OFF FROM SAT; LEVELED AT 5000 FT RWY HDG 030 DEG TO INTERCEPT THE SAT 081 DEG RADIAL; VFR TFC WAS AT OUR ALT AND 2 MI ACCORDING TO THE TCASII. WAS NOT POINTED OUT BY ATC. DELAYED TURN TILL ABOUT 1 MI PAST RADIAL WHEN ACFT HAD CLBED THROUGH OUR ALT BY 200 FT ACCORDING TO TCASII; ATC INSISTED THAT WE TURN. SMA HAD CLBED TO 5200 FT SO WE TURNED. WE WERE THEN IMMEDIATELY PLACED INTO A CONFLICT. SMA PASSED WITHIN 1/2 MI AND 100 FT OF US. WE HAD CLBED 200-300 FT DUE TO VISUAL STEEP TURN.