I do something similar with my kids. If they don't want to pick something, or feel like they can't, we flip a coin.
The coin result isn't binding, so immediately as the coin falls, they realize that they either do or do not want that result, and then can make their choice more easily.
The coin result isn't binding, so immediately as the coin falls, they realize that they either do or do not want that result, and then can make their choice more easily.