
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
A parallelepiped $PQRS$ is generated by vectors $\overrightarrow{PQ},$ $\overrightarrow{PR},$ and $\overrightarrow{PS},$ where $\overrightarrow{PQ} \cdot \overrightarrow{PR} = 0$. Compute
\[
\frac{PS^2 + QR^2 + PT^2 + QS^2}{PQ^2 + PR^2 + PS^2}.
\]

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