meditate, mediate

Meditate or meditate means to contemplate or reflect--
He would sit in the corner for hours, and meditate revenge.
Let's take a few minutes each day to meditate on ways to improve.

Meditate may also mean extended thought or contemplation used as a religious or philosophical exercise--
She goes to yoga classes, and she's learning to meditate.
To some practitioners, to meditate means to contemplate nothing, silently.

Mediate or mediate means to settle a dispute or bring about an agreement--
They are trying to agree on a neutral third party to mediate the dispute.
He tried to mediate their quarrel, but they both became angry at him.

Now that you know that, you can say--
"In an effort to mediate their dispute, she sent them each to a separate room to meditate on the problem."