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[T]he core of the practice: breathing in other's pain so they can be well and have more space to relax and open, and breathing out, sending them relaxation or whatever you feel would bring them relief and happiness. However, we often cannot do this practice because we come face to face with our own fear, our own resistance, anger, or whatever our personal pain, our personal stuckness happens to be at that moment.
At that point you can change the focus and begin to do tonglen for what you are feeling and for millions of others just like you who at that very moment of time are feeling exactly the same stuckness and misery. Maybe you are able to name your pain. You recognize it clearly as terror or revulsion or anger or wanting to get revenge. So you breathe in for all the people who are caught with that same emotion and you send out relief or whatever opens up the space for yourself and all those countless others. Maybe you can't name what you're feeling. But you can feel it —a tightness in the stomach, a heavy darkness or whatever. Just contact what you are feeling and breathe in, take it in —for all of us and send out relief to all of us.
People often say that this practice goes against the grain of how we usually hold ourselves together. Truthfully, this practice does go against the grain of wanting things on our own terms, of wanting it to work out for ourselves no matter what happens to the others. The practice dissolves the armor of self-protection we've tried so hard to create around ourselves. In Buddhist language one would say that it dissolves the fixation and clinging of ego.