
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Simplify the following expression:
\[
\left(\frac{a}{b} \sqrt[3]{b-\frac{4 a^{6}}{b^{3}}}-a^{2} \sqrt[3]{\frac{b}{a^{6}}-\frac{4}{b^{3}}}+\frac{2}{a b} \sqrt[3]{a^{3} b^{4}-4 a^{9}}\right) \div \frac{\sqrt[3]{b^{2}-2 a^{3}}}{b^{2}}
\]

Present the answer in LaTex format: \boxed{Your answer}
user