
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
Determine the value of $\frac{1}{p^2} + \frac{1}{q^2} + \frac{1}{r^2}$ if the roots of the equation $x^3 - 15x^2 + 26x + 3 = 0$ are $p$, $q$, and $r$.

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