
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 \(p\), \(q\), and \(r\) are the roots of the cubic equation \(ax^3 + bx^2 + cx + d = 0\), find the value of \(\frac{1}{p^2}+\frac{1}{q^2}+\frac{1}{r^2}\).
A) \(\frac{b^2 - 4ac}{2ad}\)
B) \(\frac{c^2 - 4bd}{d^2}\)
C) \(\frac{c^2 - 2bd}{d^2}\)
D) \(\frac{c^2 - 3bd}{d^2}\)

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