The connection between belief and action is indestructible. Actions flow from beliefs in an honest way. Actions are a more reliable indicator of what we believe even than what we ourselves think.
It is easier for us to lie to ourselves about what we believe than it is for our actions to lie about what we believe.
Rather than look at our actions and say "I don't know why I do that, because I don't believe it," we should listen to them and say "What is this action teaching me about what I believe?"
Consider this example. We may think we believe that the Gospel of Jesus Christ is the best news in the world, but perhaps we do not ever tell anyone about it. Perhaps we get much more excited about a game of sports, or winning the lottery, or the birth of a child.
Say that we actually did win the lottery. I imagine we would be excited and not a small number of people. We do speak about the things that excite us. And say that we never speak of the Gospel of Jesus Christ.
Is it really true in this case that we believe the Gospel of Jesus Christ is better and more exciting news than winning the lottery? I don't think so. If we listen to the actions, they teach us that we do indeed believe that winning the lottery was good news and exciting, and the Gospel of Jesus Christ is perhaps a somewhat intriguing idea for us to mull over, or something we might think is exciting for us, but not worth sharing with others, etc.