What assignment does Theo give to Doug Hoo?

In "The Westing Game" by Ellen Raskin, Theo Theodorakis gives Doug Hoo the assignment of observing and gathering information about their fellow heirs in the Westing game. He believes that Doug's athleticism and his ability to blend in will help them uncover clues and better understand the dynamics among the other participants. This collaboration is part of their strategy to solve the mystery surrounding Sam Westing's will.