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* Bugcheck Analysis *
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Use !analyze -v to get detailed debugging information.
BugCheck 1, {77871dea, 0, ffff, fffff88008ef8ca0}
Probably caused by : ntkrnlmp.exe ( nt!KiSystemServiceExit+245 )
Followup: MachineOwner
--------- Your crash dumps are not showing any finite probable cause. In such a situation, it is better to enable Driver Verifier to monitor the drivers.
Driver Verifier - Enable and Disable
Run Driver Verifier for 24 hours or the occurrence of the next crash, whichever is earlier.

Information
Why Driver Verifier:
It puts a stress on the drivers, ans so it makes the unstable drivers crash. Hopefully the driver that crashes is recorded in the memory dump.
How Can we know that DV is enabled:
It will make the system bit of slow, laggy.

Warning
Before enabling DV, make it sure that you have earlier System restore points made in your computer. You can check it easily by using
CCleaner looking at Tools > System Restore.
If there is no points,
make a System Restore Point manually before enabling DV.

Tip
Let us know the results, with the subsequent crash dumps, if any.
Do some Disc checks, too.
- Update your SSD's Firmware
- Reseat the sata and power.

- Run chkdsk /f/r, following the option two of the tutorial Disk Check
- Seatool for dos: SeaTools | Seagate download
Burn it in a blank cd. boot from the CD, click on "Accept", wait for it to finish detecting the drives, then in the upper left corner select "Basic Tests", then select "Long Test" and let it run.
And,
Use Microsoft Security Essentials as there are crashes, it is the most light on the system.
Uninstall AVG.
Use
Microsoft Security Essentials as your antivirus with windows inbuilt firewall, and
free MBAM as the on demand scanner.
Download and install those, and then run full system scans with both of them, one by one.
Let us know the results.