Let $a$ and $b$ be real numbers such that $a > 2b > 0.$  Find the minimum value of
\[3a^3 \sqrt{3} + \frac{2}{ab - 2b^2}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a$ and $b$ be real numbers such that $a > 2b > 0.$  Find the minimum value of
\[3a^3 \sqrt{3} + \frac{2}{ab - 2b^2}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
20
Let $a$ and $b$ be real numbers such that $a > 2b > 0.$  Find the minimum value of
\[3a^3 \sqrt{3} + \frac{2}{ab - 2b^2}.\]
train