I think there needs to be a distinction between "promotes" and "causes". Certainly in some cases the US Government has encouraged revolutions, as have independent players within the US, but no amount of encouragement is going to conjure up a revolution where the conditions to support one do not exist. In other cases the revolutions have been entirely spontaneous with little effort or knowledge on the US side. After all the talk of how the Arab Spring caught US intel agencies napping it's a bit ironic to hear that those same agencies allegedly caused the revolutions.
I don't think there's been a single "color" or "spring" revolution that could be reasonably claimed to have been caused by external intervention. I think that on the decision making level the Russians are well aware of that, though there is always the risk of falling for one's own propaganda.
That's ironic in some ways... during the Cold War the US often found itself supporting autocrats and claiming that rebellion against those autocrats was caused by Soviet subversion. Now the roles seem to be reversed. I guess it's always easier to blame an ally's troubles on foreign subversion than to concede that your ally is an A-hole.
Russia and China cooperate, but it seems well short of a coalition, and they will go their own way as they see fit. Just for one example, Russia's relationship with China does not stop the Russians from selling fairly advanced weapons systems to Vietnam, which is not exactly on friendly terms with China. It's actually interesting that the Chinese have so little to say about those sales.
Despite the cooperation, there remain areas of serious strategic competition between Russia and China, notably in Central Asia.
Not sure the Russia/China relationship requires a change in US strategy, but it would certainly be wise for the US to be prepared for potential changes and evolutions in that relationship. Any number of things could happen and I don't think anyone can really predict how it will turn.
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