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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You are a helpful assistant.<|im_end|>
<|im_start|>user
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 $a^2.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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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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