Let the image of the point $\left(\frac{5}{3}, \frac{5}{3}, \frac{8}{3}\right)$ in the plane $x-2 y+z-2=0$ be $P$. If the distance of the point $Q(6-2, \alpha), \alpha>Q$ from $P$ is 13 , then $a$ is equal to $\_\_\_\_$ .
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