How did the US Supreme Court feel about the idea of “separate but equal” in the case Plessy v. Ferguson?

Annie and bart are coworkers. in fact, they share a cubicle wall. recently, they were involved in a fender-bender in the company parking lot. each blames the other for the accident, and the two have stopped speaking. would you advise them to try to settle their dispute through arbitration, mediation, or with a traditional lawsuit? why?