
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 the value of the following expressions:

(I) ${8}^{\frac{2}{3}}+{(0.01)}^{-\frac{1}{2}}+{\left(\frac{1}{27}\right)}^{-\frac{1}{3}}$;

(II) $2\lg 5+\frac{2}{3}\lg 8+\lg 5\cdot \lg 20+{\left(\lg 2\right)}^{2}$.

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