Compute
\[\prod_{n = 0}^\infty \left[ 1 - \left( \frac{1}{2} \right)^{3^n} + \left( \frac{1}{4} \right)^{3^n} \right].\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute
\[\prod_{n = 0}^\infty \left[ 1 - \left( \frac{1}{2} \right)^{3^n} + \left( \frac{1}{4} \right)^{3^n} \right].\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{2}{3}
Compute
\[\prod_{n = 0}^\infty \left[ 1 - \left( \frac{1}{2} \right)^{3^n} + \left( \frac{1}{4} \right)^{3^n} \right].\]
train