
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
Simplify or evaluate the following expressions:

1. $((1)(2a^{\frac{1}{2}}b^{\frac{1}{3}})(a^{\frac{2}{3}}b^{\frac{1}{2}})\div(\frac{1}{3}a^{\frac{1}{6}}b^{\frac{5}{6}}))$
2. $((2)(\frac{9}{16})^{\frac{1}{2}}+10^{\lg 9-2\lg 2}+\ln 4e^{3} -\log _{9}8\cdot\log _{4} 33)$

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