The greatest compassion is to re-establish the boundaries for ourselves and others. When someone is suffering they are not seeing themselves as a complete and beautiful being that exists eternally and independently of the situation. The greatest compassion we can show someone at such a time is to hold that distinction for them, to see them as that separate and positive spiritual being, for example, if someone is angry we don't address the anger but see the real being that they are and what is really good about them.
To be able to do this for others we first need to do it for ourselves. So to really address the problem of suffering we really need to begin with getting to know ourselves.