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That screen indicates that either the system files are corrupted or the hard drive is failing.
You can reinstall your Mac OS X. Reinstalling OS X won't delete any of your files. It will just replace the corrupted system files with new one and that should fix the problem unless it is hardware related.
Restart your Mac and immediately hold down Command and R keys at the same time for 15 seconds and this will boot your Mac to the Mac OS X Utilities screen. From there, click Reinstall Mac OS X. Then follow the instructions to reinstall your Mac OS X.
If that didn't work, then restart your Mac and immediately hold down Command, Option and R keys at the same time for 15 seconds and this will boot your Mac to installation screen. Follow the onscreen instructions to reinstall.
Please let me know if that didn't work, so we can continue troubleshooting. I will send you instructions in here, so you can take your time and do the steps at your convenience.