
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
(1) Calculate the value of: $2\lg 4 + \lg \frac{5}{8} + \sqrt{(\sqrt{3} - \pi)^2}$.
(2) Given $x^{\frac{1}{2}} + x^{-\frac{1}{2}} = 3$, find the value of $x^{\frac{3}{2}} + x^{-\frac{3}{2}}$.

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