
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) $9^{\frac{1}{2}} + \left(\frac{1}{2}\right)^{-1} - \lg 100$;
(II) $\left(2a^{\frac{2}{3}}b^{\frac{1}{2}}\right)\left(-6a^{\frac{1}{2}}b^{\frac{1}{3}}\right) \div \left(-3a^{\frac{1}{6}}b^{\frac{5}{6}}\right)$.

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