
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
Given the quadratic equation $x^{2}-8x+4=0$ with two roots $x_{1}$, $x_{2}$ ($x_{1} < x_{2}$),
(1) Find the value of $x_{1}^{-2}-x_{2}^{-2}$.
(2) Find the value of $x_{1}^{- \frac{1}{2}}-x_{2}^{- \frac{1}{2}}$.

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