
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 that the quadratic equation $x^2-8x+4=0$ has two roots denoted by $x_1$ and $x_2$ (where $x_1 < x_2$),  
(1) Calculate the value of $x_1^{-2}-x_2^{-2}$.  
(2) Calculate 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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