
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 value of the following expressions:

(1) $0.001\;^{-\frac{1}{3}} - \left(\frac{7}{8}\right)^{0} + 16\;^{\frac{3}{4}} + (\sqrt{2} \cdot 33)^{6}$

(2) $\frac{2\lg{2}+\lg{3}}{1+\frac{1}{2}\lg{0.36}+\frac{1}{4}\lg{16}}$

(3) Given $x^{\frac{1}{2}}+x^{-\frac{1}{2}}=3$, find the value of $x+x^{-1}$.

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