11. For the equation $\sin ^{2} x+a \cos x-2 a=0$ with respect to $x$ to have real roots, the range of the real number $a$ is
11. $[0,4-2 \sqrt{3}]$

Let $X=\cos x, Y=\sin x$, then the original problem is transformed into the system of equations $\left\{\begin{array}{l}Y^{2}=-a(X-2), \\ X^{2}+Y^{2}=1\end{array}\right.$ having solutions, find the range of values for $a$.