
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:

(1) $\sqrt[3]{(-4)^{3}} - \left( \frac{1}{2}\right)^{0} + 0.25^{\frac{1}{2}} \times \left( \frac{-1}{\sqrt{2}}\right)^{-4}$;

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

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