
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 \( (0,0,r). \) Find
\[
\frac{PQ^2 + PR^2 + QR^2}{p^2 + q^2 + r^2}.
\]

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