
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
Find the values of the following expressions:  
$(1) 2^{-1} + 16^\frac{3}{4} - (\sqrt{2} + 1)^0 + \log_3\sqrt{3}$.  
$(2) \left(\lg 5\right)^{2} - \left(\lg 2\right)^{2} + 2\lg 2 + \log_2 9 \cdot \log_3 2$.

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