Mutually cooperate is a term that describes a situation in which two or more parties work together in order to achieve a common goal. The term can also be used to describe a situation in which two or more parties are working together in a cooperative manner. In this context, the crossword solution 'LIAISE' is an appropriate term to describe the concept of mutually cooperating. LIAISE is a verb that means to communicate and cooperate with each other in order to achieve a common goal.