Reformat / reset an unrooted phone and wipe /system

I'd like to reformat / reset my verizon Samsung S4 (SCH-I545, baseband **OF1, Android 5.0.1). After doing a number of tests and experimentation, I believe that there is a malicious binary sitting in /system which is causing me to follow a random Russian porn Instagram account. I'd like to get rid of whatever is causing the auto-follow (it's not even good porn), so I thought a hard reset / reformat would be ideal... HOWEVER, I believe that a factory reset does not touch /system. Is there a recommended approach with a non-rooted phone to essentially start with a blank slate? The phone itself was never rooted, but it did come refurbished a year or so ago from Verizon. Since it's running a OF1 baseband, I believe rooting it is out of the question? If it's possible to root, that might solve a lot of problems.