Let ABCD be a square. Points E,F,G,H are on the line segments AB,BC,CD,DA respectively such that 2AE=EB, 2BF=FC, 2CG=GD, and 2DH=HA. The area bounded by the line segments AG,BH,CE,DF is a square with side length 1. If AB can be written as ab, where a and b are positive integers such that b is square-free, find a+b.
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