B737-800 flight crew reported NMAC with another aircraft while in descent. Flight crew took evasive action.

Narrative

Descending to 10;000 feet on a vector we were at 300 kts and flight idol. We saw a potential aircraft ahead and ATC issued a turn. (which made things worse). As we started the turn we were 500 feet above the threat aircraft and received a climb RA. Complied with procedures according to training (autopilot/autothrottle off; transition smoothly from decent to a climb. We got within 100 feet vertical separation.Cause: Failure to intervene sooner. This is prohibited in training; and we flew like we were trained; which led to reduced separation. I recently completed training where SOP's and standardization were drilled into us (at the expense of being a pilot and dealing with the situation at hand). The training on this made us less safe.Suggestions: Change the way company trains pilots. What we do and compliance with checklists should be emphasized; not what we say or memorizing (see decades of NASA research on memorized tasks) flows; often at inappropriate times. The TCAS training is negative training. We are trained to wait for the RA; which is what we did; which caused a 100 foot vertical separation. Waiting for the RA to act is wrong and should NOT be part of the training.