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Are there any tools where I can post the same thing (including images, links, and/or videos) to both my Facebook page and G+ page at the same time?
There are lots of tools that will automate social media posting. The one that I have used is Hootsuit. The free account will allow you to post on three different social media sites and the paid account will let you post on 35 social media sites.
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I found an RSS service that created a feed from Google Plus page posts. Then I used Networked Blogs which is an automation tool that will post to my Facebook page. When I signed up for these services it was years ago and they were free. Since that time things have been changed and there may be a small charge for the service. But it worked quite well.
You could also try dlvr.it. There is a free plan and an upgrade.