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reconcile - To bring two or more people or groups into a state of harmony or understanding after a disagreement or conflict.

After a long argument, they managed to reconcile their differences and rebuild their relationship, realizing how much they valued each other.
grapple - To seize something and hold it firmly; to wrestle with; to ponder and intensely evaluate a problem; to struggle to deal with

When Bill got lost on his trip to Paris, he had to grapple with the task of finding a place to sleep and not knowing the language.