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

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