
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
Simplify and express with negative exponents, the expression $\left(x^2 - y^2\right)^{-1}\left(x^{-1} - z^{-1}\right)$.
**A)** $x^{-2}z^{-1}(x^2 - y^2)^{-1}$
**B)** $(z - x)x^{-1}z^{-1}(x^2 - y^2)^{-1}$
**C)** $x^{-1}z^{-1}(x^2 - y^2)^{-1}$
**D)** $x^{-2} + z^{-2}$
**E)** $\frac{1}{x^{-1}z^{-1}(x^2 - y^2)}$

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