
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 and calculate:  
(1) $(7+4\sqrt{3})^{\frac{1}{2}}-81^{\frac{1}{8}}+32^{\frac{3}{5}}-2\times\left(\frac{1}{8}\right)^{-\frac{2}{3}}+32\times(4^{-\frac{1}{3}})^{-1}$  
(2) $(\log_{6}2)^{2}+(\log_{6}3)^{2}+3\log_{6}2\times(\log_{6}318-\frac{1}{3}\log_{6}2)$．

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