LGT CLIMBING ON ASSIGNED HEADING GIVEN TRAFFIC ADVISORY ON SMA AND BOTH ACFT TOOK EVASIVE ACTION. LGT FLT CREW DISTRACTED BY ACFT PROBLEM.

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UPON INITIAL CLBOUT FROM DEN STAPLETON ARPT; WE EXPERIENCED A PRESSURIZATION PROB SO WE RECEIVED CLRNC TO LEVEL AT 10000' MSL. ATC THEN CLRED US TO INTERCEPT J17 (155 DEGS R DEN VOR) ON A 170 DEG HDG. THEN; A 260 DEG HDG WAS GIVEN. BEFORE THE TURN TO 260 DEGS WAS COMPLETED WE WERE CLRED TO MAINTAIN PRESENT HDG AND 'EXPECT ON COURSE LEAVING 13000 AND CLRED TO FL200.' WE STOPPED THE TURN AND ROLLED OUT ON A 210 DEG HDG. ATC CAME BACK WITH; 'LGT X; YOUR HDG SHOULD BE 260 DEGS.' SO WE COMMENCED THE RIGHT HAND TURN TO 260 DEGS; AND CLBING THROUGH 11700' MSL ATC CALLED TFC '1-2 O'CLOCK; LESS THAN A MILE; WBOUND; 12000'.' WE SAW THE SINGLE ENG SMA Y IMMEDIATELY AND TURNED LEFT FOR EVASIVE ACTION. SUPPLEMENTAL INFO FROM ACN 87218: AT THE TIME WE HAD DEPARTED DEN TCA TO THE S AND HAD JUST CLBED ABOVE THE CEILING OF THE TCA AND WERE BEING VECTORED TO INTERCEPT THE ARWY SBND. RECOMMEND IMPLEMENTATION OF PROGRAM TO IDENT VFR TFC IN HIGH DENSITY AREA. RECOMMEND STRONG CREW COORD SO ONE CREW MEMBER HAS POSITIVE RESPONSIBILITY FOR SEE AND AVOID/FLY AIRPLANE WHILE OTHER CREW MEMBERS WORK ON PROB. VERY IMPORTANT AT LOW ALTS. SUPPLEMENTAL INFO FROM ACN 87220: ATC ADVISED US WE COULD REMAIN AT 10000' FOR ONLY ANOTHER 7 MI. THEY THEN ASSIGNED A HDG OF 260 DEGS. THE PRESSURIZATION PROB WAS SOLVED AND WE REQUESTED A CLB. ATC THEN TOLD US TO HOLD OUR HDG. WE WERE IN THE RIGHT TURN AND ROLLED OUT ON HDG 210 DEGS. ONE MIN LATER ATC ASKED US WHAT OUR HDG WAS AND INFORMED US OUR ASSIGNED HDG WAS 260 DEGS. WE CONTINUED THE TURN TO 260 DEGS AND ONCE ON THAT HDG WERE GIVEN A CLB TO FL200. PASSING 11700' MSL ATC ISSUED A VFR TFC ADVISORY FOR TFC 1-2 O'CLOCK; LESS THAN A MILE AT 12000'; WBOUND. I SHALLOWED OUT THE CLB AND SAW TFC AT 2 O'CLOCK BTWN 1/2-1 MI. TFC WAS A SINGLE ENG PRESSURIZED SMA Y; TAN IN COLOR. TFC PASSED OFF OUR RIGHT ABOUT 100' ABOVE US. WE PASSED THE TFC BEFORE WE COULD TAKE ACTION; BUT TFC EXECUTED EVASIVE MANEUVER TO THE RIGHT AS WE PASSED IT. UPON ARR IN IAH IT TOOK 1 1/2 HRS TO CONTACT DEN TRACON. I TALKED TO THE SUPVR AND HE RECALLED THE INCIDENT AND SAID THE TFC POPPED UP ONLY SECS PRIOR TO THE ADVISORY BEING ISSUED. WHEN FLT CREWS ARE AT LOW ALTS WORKING ON PROBS THE CONCEPT OF SEE AND AVOID MUST BE STRONGLY ADHERED TO. ATC NEEDS STRONG SUPPORT FOR MANPWR AND EQUIP (WHATEVER THEY NEED); INCLUDING A VOLUNTARY OR MANDATORY PROGRAM OF VFR ACFT BEING RECOGNIZED IN OR NEAR CLOSE PROX OF A HIGH DENSITY TFC AREA.