Over the past few weeks, my Nexus 7 running 4.2 Jelly Bean has gotten incredibly slow at times. Sometimes I can count off a full five (or more) seconds for an app to open or even for something as simple as scrolling from one home screen to another. I've had the device for three or four months and it just recently started giving me problems. I hadn't installed anything new prior to noticing the problem and everything that I have installed came from the Play store, so it should all be safe. Rebooting the device does not seem to help.
What can I do to diagnose and hopefully fix this problem? This is my first Android device so I don't even really know where to start.