
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, and let \((a, b, c)\) be a fixed point. A plane passes through \((a, b, c)\) and intersects the \(x\)-axis, \(y\)-axis, and \(z\)-axis at \(A, B,\) and \(C\), respectively, all distinct from \(O\). Let \((p, q, r)\) be the center of the ellipse passing through \(A, B, C,\) and \(O\). Find
\[
\frac{a}{p} + \frac{b}{q} + \frac{c}{r}.
\]

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