
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
Parallelepiped $PQRS$ is generated by vectors $\overrightarrow{PQ},$ $\overrightarrow{PR},$ and $\overrightarrow{PS},$ as shown below. Compute
\[
\frac{PQ^2 + PR^2 + PS^2 + QR^2 + QS^2 + RS^2}{PT^2 + PU^2 + PV^2}
\]
where $T, U, V$ are the midpoints of $QR, QS, RS$ respectively.

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