TE E E * Find all real solutions to the system of equations
$$
\left\{\begin{array}{l}
x^{2}+y^{2}+u^{2}+v^{2}=4, \\
x y u+y u v+u v x+v x y=-2, \\
x y u v=-1
\end{array}\right.
$$
From equations (1) and (3), we get 
\[
\frac{x^{2}+y^{2}+u^{2}+v^{2}}{4}=1=\sqrt[1]{|x y u v|}.
\]
Since \(\frac{x^{2}+y^{2}+u^{2}+v^{2}}{4} \geqslant \sqrt[4]{|x y u v|}\) with equality holding if and only if \(|x|=|y|=|u|=|v|\), the solution to (4) is
\[
\begin{array}{c}
|x|=|y|=|u|=|v|=1 . \\
\frac{1}{x}+\frac{1}{y}+\frac{1}{u}+\frac{1}{v}=2 .
\end{array}
\]

From (2) and (3), we get
Thus, from (5) and (6), the solution to the original system of equations is
\[
\begin{array}{c}
(x, y, u, v)=(1,1,1,-1),(1,1,-1,1), \\
(1,-1,1,1),(-1,1,1,1) .
\end{array}
\]