Inside a unit square, there is an infinite series of squares, each with sides \(\frac{3}{4}\) of the sides of the square one size larger. Their positions are at the top, on the right, at the bottom, on the left, at the top again, and so on, centered on the side they are on. As the size of the squares goes to zero, their location converges to a point \((x, y)\), where the origin of the coordinate system is the lower left corner of the original square.

If the ratio \( \dfrac xy\) can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, submit your answer as \(a+b\).

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