
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 $r$, $s$, and $t$ be real numbers, where $s \neq 0$, and let $P$, $Q$, and $R$ be points such that the midpoint of $\overline{QR}$ is $(r,0,s),$ the midpoint of $\overline{PR}$ is $(0,s,t),$ and the midpoint of $\overline{PQ}$ is $(r,s,0).$  Find
\[
\frac{PQ^2 + PR^2 + QR^2}{r^2 + s^2 + t^2}.
\]

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