While Dave is known to spend a lot of his time investigating things around his home, Jack can also be active in this area. Sometimes he investigates invading bugs, or drafts of wind, or the blinds on the window. Other times he investigates Dave and whatever shenanigans he is pulling off at the moment. Other times still, Jack kicks Dave off of a napping spot so Jack can investigate its softness. You can see the aftermath of one such occurrence here.
When he is in this mode, Jack thinks of himself as Action Jackson.