If the system of linear equations.
$$
\begin{aligned}
& 8 x+y+4 z=-2 \\
& x+y+z=0 \\
& \lambda x-3 y=\mu
\end{aligned}
$$
has infinitely many solutions, then the distance of the point $\left(\lambda, \mu,-\frac{1}{2}\right)$ from the plane $8 x+y+4 z+2=0$ is
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