
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 has a distance of 2 from the origin and intersects the $x$-axis, $y$-axis, and $z$-axis at $A$, $B$, and $C$, respectively, where $A = (\alpha, 0, 0)$, $B = (0, \beta, 0)$, and $C = (0, 0, \gamma)$, all distinct from $O$, and $\alpha + \beta + \gamma = 6$. Let $(p, q, r)$ be the centroid of triangle $ABC$. Find
\[
\frac{1}{p^2} + \frac{1}{q^2} + \frac{1}{r^2}.
\]

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