Rand tries to escape before the Amyrlin Seat can find him, but someone’s already two steps ahead.
Everyone else in the fortress is buzzing with excitement over the Amyrlin Seat’s arrival. Rand, meanwhile, is quietly shitting bricks. Step one of his escape plan is to hurry back to his room on the pretense that he needs to make himself presentable. When he arrives, the room is already a flurry of activity. Servants are busy throwing out Rand’s old clothes and replacing them with new ones, under Moiraine’s orders. He shoos the servants out of the room, hastily dresses and packs, and heads for the stables.
Rand chooses a route that takes him directly through the courtyard where the Amyrlin Seat is being received. His reasoning? It’s the shortest route — plus, what harm could there be in just looking? Says the guy who once tripped into a royal garden and nearly got arrested while trying to catch a glimpse of Logain.
Rand gets through the courtyard without incident, but the stable is where the plan starts going sideways. The groomsman tells him that an order came through just minutes ago to not allow any horses to leave the stables. Don’t worry, Rand — I’m sure this is just standard stable lockdown procedure, and the pedestrian exits will be wide open.