
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: $$3(-4)^{3} - \left(\frac{1}{2}\right)^{0} + 0.25^{\frac{1}{2}} \times \left(\frac{-1}{\sqrt{2}}\right)^{-4};$$  
(2) Given $x^{\frac{1}{2}} + x^{-\frac{1}{2}} = 3$, find the value of $$\frac{x^{2} + x^{-2} - 2}{x + x^{-1} - 3}.$$

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