
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
\[
\left(\sqrt[3]{\frac{8 z^{3}+24 z^{2}+18 z}{2 z-3}}-\sqrt[3]{\frac{8 z^{2}-24 z^{2}+18 z}{2 z+3}}\right)-\left(\frac{1}{2} \sqrt[3]{\frac{2 z}{27}-\frac{1}{6 z}}\right)^{-1}
\]

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