
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
\[ A=\frac{\sqrt[3]{8 x-y-6\left(2 \sqrt[3]{x^{2} y}-\sqrt[3]{x y^{2}}\right)} \cdot\left(4 x^{2 / 3}+2 \sqrt[3]{x y}+y^{2 / 3}\right)}{8 x \sqrt[3]{y}-y^{4 / 3}} \]

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