I had the same thing happened with my nexus, full on demonic possession, started texting, emailing, web searching, installing, installing, powering off and on, then the texting became full on conversations, followed by countless factory resets including full on system wipes when done there was nothing on the phone, no icon symbols, nothing just a flashing dot and then the phone would power off.
Then five minutes, maybe ten maybe longer it would power back on.
It did this for twelve hours on it's own. The end came when it did a factory reset followed by a serious weird flashing colors some long weird text and then it powered off and never turned back on. The following day i switched to the LG G6.
