Round about

Algebra Level 4

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?