Or must you discard a Goal/Action if you have one, and a random card only if you don’t?
A: Players get to choose. They may either look at their cards and select a Goal/Action to give up, or they may select a random card from their hand to give up. Of course, if they don’t have any Goals/Actions, they can only opt to lose a random card.
Note that random means RANDOM. They don’t get to decide which card they give up in this case. They can do this either by mixing their own hand face down, and pulling one out without looking, or they can have you pull one from their hand as they hold it up facing themselves.