If $a$ and $b$ are real numbers, $a^2b^3=\frac{32}{27}$, and $\frac{a}{b^3}=\frac{27}{4}$, what is $a+b$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $a$ and $b$ are real numbers, $a^2b^3=\frac{32}{27}$, and $\frac{a}{b^3}=\frac{27}{4}$, what is $a+b$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac83
If $a$ and $b$ are real numbers, $a^2b^3=\frac{32}{27}$, and $\frac{a}{b^3}=\frac{27}{4}$, what is $a+b$?
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