
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 $P,$ $Q,$ $R$ be points such that the midpoint of $\overline{QR}$ is $(p,0,0),$ the midpoint of $\overline{PR}$ is $(0,q,0),$ and the midpoint of $\overline{PQ}$ is $(0,0,r).$ Determine the value of
\[\frac{PQ^2 + PR^2 + QR^2}{p^2 + q^2 + r^2}.\]

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