Let $z$ be a complex number such that
\[|z - 12| + |z - 5i| = 13.\]Find the smallest possible value of $|z|.$
Question:
Let $z$ be a complex number such that
\[|z - 12| + |z - 5i| = 13.\]Find the smallest possible value of $|z|.$
Answer:
Let's think step by step.

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\frac{60}{13}
Let $z$ be a complex number such that
\[|z - 12| + |z - 5i| = 13.\]Find the smallest possible value of $|z|.$
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