
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 $((\lg 2)^{2}+\lg 5\cdot \lg 20+(\sqrt{2016})^{0}+0.027^{\frac{2}{3}}\times (\frac{1}{3})^{-2})$
(2) Given $\frac{3\tan \alpha }{\tan \alpha -2}=-1$, find the value of $\frac{7}{{{\sin }^{2}}\alpha +\sin \alpha \cdot \cos \alpha +{{\cos }^{2}}\alpha }$.

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