First answer: ZOO
Trace ZOO through these cells: 1 at row 2, column 3; 2 at row 1, column 3; 3 at row 1, column 4. Reading the letters in that order gives Z, then O, then O. All three positions are orthogonally connected, so the short answer can be checked without making a diagonal jump.
Start by moving up once, then turn right once. The route therefore has one turn and two straight segments, spanning two rows and two columns. It visits the board edge twice without entering a corner. Both its starting cell and ending cell have two open orthogonal neighbors on the raw board.
This route distinguishes the adjacent pair of Os it needs from the board's third O. Once its three cells are assigned, 17 open cells remain. That remainder agrees with the combined lengths of the next three answers, giving you a useful accounting check before you continue.