I think you might be misunderstanding the meaning of agape. It's not love that gives and expects nothing in return. Rather, it's a perfect, selfless, holy kind of love that we as humans cannot achieve. It's the kind of love that God has for us, but we can never hope to return it.
As far as it being an "action love", just look at what God did for us. He had his Son come down and be born as one of us lowly, pathetic humans. Then He let this same Son be persecuted by those self-same humans who He had come to save! The Son was beaten and then left to die on a cross, which is one of the most painful ways to die. And after all that, God even turned his back on his Son so that He could take on the sins that we have committed, all so that WE could be forgiven.
If that isn't agape in action, I don't know what is.