
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
Calculate:

1. $(1)\left( \sqrt[3]{2} \times \sqrt{3}\right)^{6}+\left( \sqrt{2 \sqrt{2}}\right)^{ \frac{4}{3}}-4\left( \dfrac{16}{49}\right)^{- \frac{1}{2}}- \sqrt[4]{2}\times{8}^{0.25}-\left(-2009\right)^{0} $

2. $2\left(\lg \sqrt{2}\right)^{2}+\lg \sqrt{2}+\lg 5+ \sqrt{\left(\lg \sqrt{2}\right)^{2}-\lg 2+1} $

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