My iPod touch won't turn on, but I can't restart it because my home button is broken.

I have an iPod touch 5th gen with the latest iOS update. It was working fine before, but when I tried to turn it on the screen stayed black. This has happened before and I restarted it, and everything has worked since. However, between now and then, my home button has stopped working and I have been using Assistive Touch. Since it will not turn on, I cannot use Assistive Touch to restart it.