
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
When further simplified and using negative exponents, what is the expression $(x + y)^{ - 2}(x^{ - 1} + y^{ - 1})^2$ equal to?
**A)** $\frac{x^{-2} + 2x^{-1}y^{-1} + y^{-2}}{x^{2} + y^{2}}$
**B)** $\frac{x^{-2} + 2x^{-1}y^{-1} + y^{-2}}{x^{2} + 2xy + y^{2}}$
**C)** $\frac{x^{-1}y^{-1}}{(x + y)^2}$
**D)** $\frac{x^{-2} + y^{-2}}{x^{2} + y^{2}}$
**E)** $\frac{1}{x^{-2} + y^{-2}}$

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