Stand on this common ground as a stronger platform from which to work out respective differences. Sort out interpretations from facts. Never ask people who have been in a fight what happened. You'll get their interpretation, their opinion, their version of what occurred. Then you get perceptions that are much closer to facts, not merely opinions.
Facts help clarify perceptions, which is basic to conflict dissolution.
Develop a sense of forgiveness. Reconciliation is impossible without it. Learn to listen actively. Take the first step toward reconciliation by being willing to listen with the intention to understand, and by being willing to listen first. Purify your heart.