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Plesk log shows:

ERROR: Failed to run the Yum utility.
The Yum utility failed to install the required packages.
Attention! Your software might be inoperable.
Please, contact product technical support.

Resolution:

Check for the atomic repo and disable it.

cd /etc/yum.repos.d/
nano atomic.repo
# Name: Atomic Rocket Turtle RPM Repository for CentOS / Red Hat Enterprise Lin$
# URL: http://www.atomicrocketturtle.com/
# Note: This isn't covered by ASL support. -Scott
[atomic]
name = CentOS / Red Hat Enterprise Linux $releasever - atomicrocketturtle.com
mirrorlist = http://www.atomicorp.com/mirrorlist/atomic/centos-6-$basearch
#mirrorlist = http://www.atomicorp.com/channels/atomic/centos/6/mirrors-atomic
enabled = 1
priority = 1
protect = 0
gpgkey = file:///etc/pki/rpm-gpg/RPM-GPG-KEY.art.txt
gpgcheck = 1

Set enabled = 1 to enabled = 0
Then run:

yum update --enablerepo=atomic atomic-release

This should resolve the error.

Or…

/usr/local/psa/admin/sbin/autoinstaller --select-release-current --reinstall-patch --install-component base

or…

yum upgrade atomic-release 

Other resources: http://kb.odin.com/en/116189