Defining empathy with no mention of compassion? To have human empathy for another is to take some action, no matter how small, while echoing the feeling itself.
My understanding is: Sympathy is the furthest removed, not much past acknowledgement of. Empathy is simply that you are able to put yourself in their position and understand logically, often "feeling" for them. The feelings in the other steps have not yet converted to emotions, so the emotion has not moved you to compassion yet, compassion is the next, but distinct phase, and it is typically coupled emotion resulting in an action.
Psychology recognizes compassion as one element of one kind of empathy. Sometimes it even separates it into it's own separate type of empathy, compassionate empathy.