
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
Let \(O\) be the origin. A variable plane is at a distance of 2 from the origin and intersects the \(x\)-axis, \(y\)-axis, and \(z\)-axis at points \(A\), \(B\), and \(C\) respectively, none of which are \(O\). Let \((p,q,r)\) be the centroid of triangle \(ABC\). Find the value of
\[\frac{1}{p^2} + \frac{1}{q^2} + \frac{1}{r^2}.\]

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