设实矩阵 $A=\left(\begin{array}{cc}a+1 & a \\ a & a\end{array}\right)$, 若对任意实向量 $\alpha=\left(\begin{array}{l}x_1 \\ x_2\end{array}\right), \beta=\left(\begin{array}{l}y_1 \\ y_2\end{array}\right)$, $\left(\alpha^T A \beta\right)^2 \leq \alpha^T A \alpha \cdot \beta^T A \beta$ 都成立, 则 $a$ 的取值范围是