
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: $$\left(\left(3 \frac{13}{81}\right)^{-3}\right)^{ \frac{1}{6}} - \lg \frac{1}{100} - \left(\ln \sqrt{e}\right)^{-1} + 0.1^{-2} - \left(2+ \frac{10}{27}\right)^{- \frac{2}{3}} - \left( \frac{1}{2+ \sqrt{3}}\right)^{0} + {2}^{-1-{\log }_{2} \frac{1}{6}} $$
(2) Given $\tan \left(\pi-\alpha\right)=-2 $, find the value of ${\sin }^{2}\left(\pi+\alpha\right)+\sin \left( \frac{\pi}{2}+\alpha\right)\cos \left( \frac{3\pi}{2}-\alpha\right)$.

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