Problem $2,(25$ Pts$)$ In a complex political landscape, a diplomat is navigating the intricate corridors of power in a foreign nation. The diplomat finds herself at a critical juncture, needing to choose the right policy path that will lead to a successful negotiation with the government. In this delicate situation, she encounters three political advisors, each from a different faction within the government: one who always tells the truth, one who always lies, and one who gives completely unpredictable answers. Unfortunately, the diplomat doesn't know which advisor belongs to which faction.

To make matters more complicated, the diplomat is permitted to ask only two yes$-$or$-$no questions, and each question must be directed to a single advisor. Can the diplomat figure out which policy path will lead to a successful negotiation?

Bonus question $(10$ Pts$)$ Describe the situation using first$-$order logic and formally prove that your strategy is valid.