
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 $p$, $q$, and $r$ be real numbers, and let points $A$, $B$, and $C$ be in space such that the midpoint of $\overline{BC}$ is $(p,0,1)$, the midpoint of $\overline{AC}$ is $(0,q,1)$, and the midpoint of $\overline{AB}$ is $(0,0,r)$. Find the ratio $\frac{AB^2 + AC^2 + BC^2}{p^2 + q^2 + r^2}$.

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