Actions speak louder than words.

This saying means that actually taking an action is more important than what you say.

I agree with what the proverb implies.
I think that it’s so easy to say what sounds nice or good or even seems socially acceptable that what he says means little.
We can’t simply believe someone’s words.

For example, we tend to judge a person by his very action when his words and actions are different. 聼起來自然嗎?

Actions speak louder than words.

This saying means that what you do is more important than what you say. (this one sounds better because it uses the "what you ___" structure for both of the things you are comparing.)
or
This means that your opinions and beliefs are shown more clearly in your actions than in your stated opinions and beliefs. (This is how I would put it.)

I agree with what the proverb implies.
Especially when it comes to socially accepted and expected beliefs, simply saying that you believe them is almost meaningless. You could just be saying so because of social pressure. The way you act tells the real story.