Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates $(-2, 1)$ and arrived in the Iron Hills at the point with coordinates $(-1, 6)$. If he began walking in the direction of the vector $\mathbf{v} = 5 \mathbf{i} + 2 \mathbf{j}$ and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn.

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