
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: $$0.008^{- \frac {1}{3}}+81^{ \frac {1}{2}}+\log_{ \sqrt {2}} \sqrt { \frac {1}{16}}$$;  
(2) Solve the equation: $$\lg x \cdot \lg \frac {x}{100}=3$$.

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