My iPhone screen suddenly goes black with circle waiting animation at the center. I forced restart it. And now it can't get past loading screen I was working, when I noticed my phone screen suddenly goes black with the familiar white circle animation. I can't do anything to my phone (and I'm now afraid it was a forced iOS system upgrade). After waiting for a moment, I decided to force restart it (press power + home) because even an iOS system upgrade doesn't take that long in the waiting screen. The iPhone restarted, showing its usual black apple on white background logo. But I have waited for 5 minutes and there's no sign of it will ever finished. I restarted it again, but the result is the same. What should I do?
I think a restore might be in order. 

First I would plug it on a Mac or PC with an USB cable and do a full encrypted backup. I suppose iTunes will still be able to back it up, but it might require you to authorize its access on the iPhone itself, in which case you'all have to rely on an iCloud Backup restore after the software restore.