You have quoted the right verses, but "Prayer + appropriate tangible action = desired result"????
God’s rule of the universe does not annul in favor of those who pray or do not pray. He already supplied the idea of appropriate action creating appropriate results like,
Jump from 30th floor = Go to a grave.
Though prayer may create good effects (feeling better, communion with God, or look good in the eyes of other, etc.) on the mind of those who pray, but choosing right thing and right doing has nothing to do with it. It only needs a capable mind. Otherwise, there have been so many prayers in the world already since time immemorial. What results?