The exit is in the middle of the map. There's a narrow path that's rather hidden. Note that if you explore the area map that you enter this area at around the NW of the map and the accessable area itself ends up looks like a big "U". Go to the bottom of the "U", the bottom of the map, move a bit to the East and start looking at the black area in the middle/bottom of the "U". You'll eventually find the hidden path.
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