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In Finder, click on Go menu and select Computer. Open Macintosh HD. Open Library folder. You will find a folder named Updates in there. You will see several folders and files in there. Open all folders and check for a file starting with Safari
It is a package file. Open it and follow the onscreen instructions to install it. That should update Safari.
Then click on Apple menu > App Store. In App Store, click on Updates tab and do all software updates in there.
Please let me know if that didn't work, so we can continue troublehsooting.