Round about

Algebra Level 5

A set of four distinct real numbers is called round if it satisfies \[ \begin{cases} x_1^2+x_2=2,\\ x_2^2+x_3=2,\\ x_3^2+x_4=2,\\ x_4^2+x_1=2,\\ \end{cases} \] and \( x_1 = \min (x_1, x_2, x_3, x_4 ) \).

How many round sets are there?

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