
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
Calculate the value of the following expressions:

(I) $a\sqrt{a} \cdot (\frac{1}{a} - \frac{1}{\sqrt{a^3 b}}) \div \frac{a - b^{-1}}{\sqrt{a} + b^{-\frac{1}{2}}}$; ($a > 0, b > 0$)

(II) $\log_{9} \sqrt{27} + \sqrt{4 \log_{2} 3} - \log_{2} 12 + \log_{2} 3$.

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