
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
Evaluate:

1. ${{\left( \dfrac{27}{8} \right)}^{-\frac{2}{3}}}-{{\left( \dfrac{49}{9} \right)}^{0.5}}+{{(0.008)}^{-\frac{2}{3}}}\times \dfrac{2}{25}$;

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

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