
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 $(2a, 2b, 2c)$ be a fixed point. A plane passes through $(2a, 2b, 2c)$ and intersects the $x$-axis, $y$-axis, and $z$-axis at points $A$, $B$, and $C$, respectively. Assume none of these points coincides with $O$ and let $(p, q, r)$ be the center of the sphere passing through $A$, $B$, $C$, $O$. Find the value of $\frac{a}{p} + \frac{b}{q} + \frac{c}{r}.$

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