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My 5s also crashed today and needed to be jump started by iTunes after closing apps ( have thread in here) it's also blue screened but stayed on when opening safari.

Ios7:0:2 seems to be crap!
 
Blue Screen auto reboot on new iPhone 5S

I just got my 5S iPhone yesterday afternoon and it seemed to work fine. Today I've had 3 Blue Screens then it reboots. They were at different times doing different things. I was moving an app to another screen one time. I was opening a document in Pages another time. I can't seem to recreate it but the only answer Apple had was to restore. The last time I did that on my 4S it took HOURS to get all of my stuff back. Not willing yet to take that step, yet. Hopefully it is the IOS upgrade & it will get fixed. Other than that I LOVE IT! :)
 
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