
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
Evaluate the expression:
\[ \left(\frac{3^{3/2}+\frac{1}{8} \cdot z^{3/5}}{3+\sqrt{3} \cdot \sqrt[5]{z}+\frac{1}{4} \sqrt[5]{z^2}}+\frac{3 \sqrt{3} \cdot \sqrt[5]{z}}{2 \sqrt{3}+\sqrt[5]{z}}\right)^{-1} \div \frac{1}{2 \sqrt{12}+\sqrt[5]{32z}}. \]

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