4. Find the smallest value of the parameter $a$, for which the system of equations

$$
\left\{\begin{array}{c}
\sqrt{(x-6)^{2}+(y-13)^{2}}+\sqrt{(x-18)^{2}+(y-4)^{2}}=15 \\
(x-2 a)^{2}+(y-4 a)^{2}=\frac{1}{4}
\end{array}\right.
$$

has a unique solution

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