
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:
(1) $4(3-\pi)^4 + (0.008)^{-\frac{1}{3}} - (\frac{1}{4})^{\frac{1}{2}} \times (\frac{1}{\sqrt{2}})^{-4}$
(2) If $x^{\frac{1}{2}} + x^{-\frac{1}{2}} = \sqrt{7}$, find the value of $\frac{x+x^{-1}}{x^2+x^{-2}-3}$.

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