Let $a,$ $b,$ and $c$ be positive real numbers such that $a^2 = bc$ and $a + b + c = abc.$  Find the smallest possible value of $a^2.$
Question:
Let $a,$ $b,$ and $c$ be positive real numbers such that $a^2 = bc$ and $a + b + c = abc.$  Find the smallest possible value of $a^2.$
Answer:
Let's think step by step.

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3
Let $a,$ $b,$ and $c$ be positive real numbers such that $a^2 = bc$ and $a + b + c = abc.$  Find the smallest possible value of $a^2.$
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