
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
$(1)$ Calculate $\sqrt[3]{(-4)^3}-(\frac{1}{9})^{-\frac{3}{2}}+(\sqrt[3]{3}×\sqrt{2})^6$;<br/>$(2)$ Simplify $\sqrt[3]{a^{\frac{5}{2}}\sqrt{a^{-3}}}÷\sqrt{\sqrt[3]{a^{-8}}•\sqrt[3]{a^2}}(a>0)$.

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