Question 119
Given the line $L: x + y - 9 = 0$ and the circle $M: 2x^2 + 2y^2 - 8x - 8y - 1 = 0$, point $A$ is on $L$ and points $B, C$ are on $M$; $\angle BAC = 45^\circ$ and the line $AB$ is through the center of $M$. Then the range of the $x$ coordinate of point $A$ is ______.