
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: ${4}^{\frac{3}{2}}+(\sqrt{2} \times \sqrt[3]{3})^{6}-16 \times {(2\frac{10}{27})}^{-\frac{2}{3}}$;  
$(2)$ Calculate: ${3}^{\log_{3}2}-\frac{2}{3}\log_{2}3 \cdot \log_{3}8+\frac{1}{3}\log_{6}8+2\log_{6}\sqrt{3}$.

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