The parties could be asked to formulate a joint statement describing the current situation. That is, before pressing them to adopt a jointly acceptable solution to their dilemma, it can be useful to first ask them to come to a jointly acceptable formulation of that dilemma. The exercise of formulating a new joint account of the situation can be understood as an effort to remake the meaning of the situation, a jointly negotiated meaning. Meanings are not inherent in things, but are socially negotiated. Meaning is always subjective.
Conflict is like art.
The parties should not see themselves as helpless victims of it. They participate in the construction of it. They have the potential for deconstructing and reconstructing it as well. Being compelled to accept others' interpretation of things is a sign of disempowment. An art teacher who tells students the meaning of a painting and then quizzes them to see if they can reproduce that answer is a bad teacher.