They say, "It's not what you say, it's how you say it." To that we could add: "It's why you say it." What's the intention behind your words? Your intention, more than anything else, will determine your impact on others.
Intention makes action what it is. Intention is the only difference between a knife in the hand of a surgeon, or a knife in the hand of a murderer. Intention affects everything you do. You could give someone a flower to appease or manipulate them, and that would feel terrible. Or you could give someone a flower because you love them, and that would make them happy. The intention behind the action makes the difference.
Now you see what love has to do with right action: love makes action right. Right action is action with love behind it (with no other, more important intentions dominant in the mix). Whatever we do in a spirit of sincere love will surely be beneficial, healing, uplifting -- and right.
And finally: right action makes love true. Talk is cheap, and so is mere sentiment. But when we put love into action, we get traction. Love in action means far more to others than the love we feel, but don't actively express. Thus, it is correct to say, right action is love.
Such is the connection between Love and Right Action.