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Algebra Level 5

\[\left\{\begin{matrix} x^8-28y^2x^6+70x^4y^4-28y^6x^2+y^8=\frac{\sqrt{3}}{2} & & \\ 8yx^7-56y^3x^5+56y^5x^3-8y^7x=\frac{1}{2} & & \end{matrix}\right.\] How many pairs of \((x,y)\) satisfy this system of equation above?

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