Just saw the movie--Jack Reacher's style is very much that of the Westerosi hedge knight. So, he goes walking and gets lost. Points if he meets up with Sandor trying to protect Arya, Brienne and Jaime in search of the Stark girls or Petyr trying to hire some sellswords in Gulltown. And then just take it from there--maybe Jack is able to: get medical aid for Sandor and keep Arya from running away; help Brienne and Jaime in their investigation or rescue Sansa and give Petyr a dose of his own medicine.