
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 expression: 

\[
\sqrt[3]{\frac{2 x^{2}}{9+18 x+9 x^{2}}} \cdot \sqrt{\frac{(x+1) \sqrt[3]{1-x}}{x}} \cdot \sqrt[3]{\frac{3 \sqrt{1-x^{2}}}{2 x \sqrt{x}}}.
\]

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