
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 with the equation \( x + 2y + 3z = 6 \) 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 sphere 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}
user