
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
If \(xy = 2c\) and \(\frac{1}{x^2} + \frac{1}{y^2} = 3a\), then find the value of \((x + y)^2\).
A) \(12ac^2 + 2c\)
B) \(12ac^2 + 4c\)
C) \(6ac^2 + 4c\)
D) \(3ac^2 + 2c\)

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