Tapered mates for movement

I have an assembly that I'm having trouble getting to react the way I want it to. I have one part with an outside taper to it and another with an inside taper to it. I wan to mate them so that when I slide the outside part forward linearly, the inner one moves down linearly. I want this to behave like a collet in real life terms. I've tried the coincident mate for the tapered surfaces but then it just locks both parts in place. I attached a simplified example of what I am trying to do. 

SolidworksAssemblies