How can I get a custom UIControl to participate in a segue as a push action?

I have a custom class that inherits from UIControl, to get touch events. It's basically a collection of other controls that acts as one. I'm converting my app from xibs to a storyboard. It's been mostly painless, except for this.

I drag a UIView into my scene, change the class to my custom control, hook it up to outlets on my ViewController. What I want to do with the control when it's clicked is perform a (push) segue to another ViewController. But the outlets in the designer aren't there for my UIControl to set up the segue.

Is it possible to do this? If so, what do I do to the class to enable that?