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The future tense is will conciliate.
Conciliate means to appease, to try to reconcile, to try to gain good will. Here are some sentences.
1. Cause to be more favourably inclined; gain the good will of:
Sarah manged to conciliate the angry customer.
2. Make (one thing) compatible with (another):
Jack had to conciliate the new results with the existing theories.
The two opposing sides could not agree to stop fighting and so a conciliator was brought in to calm things down and conciliate an agreement.
Sandra used her womanly charm to conciliate an angry competitor.