Kat didn't sleep. She didn't meditate either. When the early morning came around and Xiang woke up, Kat just informed him he could go back to sleep. Kat had sent of a message to everyone, just to let them know she was fine. It might have been stretching the truth a bit, but it wasn't a lie certainly.
Kat didn't really know where her thoughts wanted to go. They seemed to hover around the events of yesterday, but do everything they could not to address the elephant in the room. Kat, at one point after insisting Xiang get more sleep, tried to force herself to confront the problem. She replayed the scene over in her mind half a dozen times… but it didn't really help.