FLC OF A B727 MISUNDERSTOOD DEP CLRNC AFTER VECTORS DURING DEP ON A SID ROUTING RESULTING IN A TCASII RA AND EVASIVE ACTION BY STOPPING THEIR CLB.

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WE WERE DEPARTING ONT FLYING THE PRADO 4 DEP. AT THE TIME; WE WERE FLYING RADAR VECTORS FOR TFC. AT APPROX XA00 LCL TIME; THE DEP CTLR ISSUED US A CLRNC TO 'FLY A 100 DEG HDG TO INTERCEPT THE THERMAL TRANSITION ON THE DEP; E OF THE PDZ 130 DEG RADIAL.' I READ BACK THIS CLRNC AND PROCEEDED TO ACTIVELY WATCH FOR TFC BOTH VISUALLY AND WITH THE USE OF TCASII. THE CAPT WAS FLYING; AND WAS CONFUSED AS TO THE CTLR'S INTENTIONS WITH THIS CLRNC. HE ASKED ME TO CLARIFY OUR CLRNC; BUT THE FREQ WAS SO BUSY THAT I COULDN'T GET A WORD IN. THE CAPT UNDERSTOOD THE CLRNC TO MEAN THAT HE SHOULD FLY THE 100 DEG HDG TO INTERCEPT THE PDZ 130 DEG RADIAL. I UNDERSTOOD THE CLRNC TO MEAN THAT WE SHOULD FLY THE 100 DEG HDG TO INTERCEPT THE TRM 263 DEG RADIAL. (APPARENTLY BOTH INTERPS ARE INACCURATE BECAUSE AFTER LOOKING AT THE DEP; THE ONLY POSSIBLE WAY TO NAV AN INTERCEPT OF THE TRM 263 DEG RADIAL FROM OUR POS IS TO INTERCEPT THE SLI 080 DEG RADIAL TO THE 59 DME CHANGEOVER POINT. THEN WE COULD FLY TO TRM VIA THE 263 DEG RADIAL.) AS THE CAPT FLEW HIS OWN MENTAL INTERP OF OUR CLRNC (WITHOUT VERBALIZING); HE INTERCEPTED THE PDZ 130 DEG RADIAL AND WE ENCOUNTERED A TCASII RA OF AN ACFT 500 FT ABOVE US AND 3 MI. WE DISCONTINUED OUR CLB; VISUALLY AVOIDED THE TFC; AND THEN RESUMED OUR CLB. THE CTLR THEN CONTACTED US TO ASK IF WE WERE STILL CLBING. I TOLD HIM THAT WE RECEIVED AN RA; AND DISCONTINUED THE CLB. THE CTLR SAID THAT WE WERE TO INTERCEPT THE TRM 263 DEG RADIAL (NOT POSSIBLE FROM OUR POS) IN ORDER TO AVOID THAT TFC. I SAID THAT WE MISUNDERSTOOD THE CLRNC. WE WERE UNABLE TO CLARIFY THE CTLR'S INTENTIONS OF OUR ORIGINAL CLRNC DUE TO FREQ CONGESTION; AND ALL OF THE TFC WE WERE TRYING TO VISUALLY AVOID IN THAT AIRSPACE. FACTORS: VAGUE CLRNC; CREW MISCOM; FREQ CONGESTION; GA ACFT FLYING IN DEP CORRIDORS OF BUSY ARPTS.