
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 calculate the following expressions: 
(1) $16^{-\frac{1}{2}} - (\frac{1}{2})^{-\frac{1}{2}} - (\frac{27}{8})^{\frac{2}{3}} + (\frac{3}{5})^{0} + 4(1 - \sqrt{2})^{4}$;  
(2) $(a^{\frac{2}{3}}b^{\frac{1}{2}}) \times (-3a^{\frac{1}{2}}b^{\frac{1}{3}}) ÷ (\frac{1}{3}a^{\frac{1}{6}}b^{\frac{5}{6}})$.

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