How do you solve this?

Algebra Level 3

{(1+x)(1+x2)(1+x4)=1+y7(1+y)(1+y2)(1+y4)=1+x7\begin{cases} (1+x)(1+x^2)(1+x^4) = 1+y^7 \\ (1+y)(1+y^2)(1+y^4) = 1+x^7 \end{cases}

How many ordered pairs of real numbers (x,y)(x, y) satisfy the above equations?

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