
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
Compute the following expressions:

(1) $({a^{\frac{{3}}{{2}}}}{b^{\frac{{1}}{{2}}}})(-{3}{a^{\frac{{1}}{{2}}}}{b^{\frac{{1}}{{3}}}}) \div (\frac{{1}}{{3}}a{b^{\frac{{5}}{{6}}}})$;

(2) ${\log _4}3 \cdot {\log _9}2 - {\log _{\frac{1}{2}}}\sqrt[4]{32}$.

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