Option 1: You can go up through the Cottons and Brittons (Ferns), turning left. You'll meet up pretty soon with the Great Western Road (after some ducking and diving under branches).

 

Option 2: Head back to the Great Western Road. 

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Keep going up the Great Western Road. Eventually, you'll spy a great stone staircase. And at the top of the staircase you'll see a mysterious stake in the ground with some arrows on it.

 

Multiply the number of steps with the number of arrows to get the next password..