
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 $(5\frac{1}{16})^{0.5}-2×(2\frac{10}{27})^{-\frac{2}{3}}-2×(\sqrt{2+π})^{0}÷(\frac{3}{4})^{-2}$;<br/>$(2)$ Calculate ${3}^{log_{3}2}-2log_{2}3⋅log_{27}8+\frac{1}{3}log_{6}8+2log_{6}\sqrt{3}$.

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