
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
Simplify and evaluate the following expressions:

1. $(1) \sqrt{2 \frac{7}{9}} + 0.1^{-2} - \pi^{0} + \frac{1}{3}$
2. $(2) (\log_2 2)^{2} + \log_2 2 \log_2 5 + \sqrt{(\log_2 2)^{2} - \log_2 4 + 1}$

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