
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 \(xy = k\) and \(\frac{1}{x^2} + \frac{1}{y^2} = c\), find the value of \((x - y)^2\).
**A)** \(c^2k^2 - 2k\)  
**B)** \(ck^2 + 2k\)  
**C)** \(ck^2 - 2k\)  
**D)** \(\frac{1}{c} - 2k\)

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