
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 \( xy = a \) and \( \frac{1}{x^2} + \frac{1}{y^2} = c \), what is the value of \( (x+y)^2 \)?
**A)** \( ac^2 + a \)  
**B)** \( a^2 + c^2 \)  
**C)** \( 2ac^2 + a \)  
**D)** \( ac^2 + 2a \)  
**E)** \( c^2 + 2a \)

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