"Acting on" means taking action because of information, advice, orders, or a feeling. It can also mean having an influence on something, as when a drug is acting on the brain.
What lead me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing else but an electric field. Albert Einstein
I am a soldier, convinced that I am acting on behalf of soldiers. Siegfried Sassoon
The true measurement of a person's worth isn't what they say they believe in, but what they do in defense of those beliefs. If you're not acting on your beliefs, then they probably aren't real. Edward Snowden
The lesson I was learning involved the idea that I could feel compassion for people without acting on it. Melody Beattie
It stands to the everlasting credit of science that by acting on the human mind it has overcome man's insecurity before himself and before nature. Albert Einstein
God is acting on your soul all the time, whether you have spiritual sensations or not. Evelyn Underhill