
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 $PQRS TUVW$ is generated by vectors $\overrightarrow{PQ},$ $\overrightarrow{PR},$ and $\overrightarrow{PT},$ as defined below. Compute the ratio:
\[\frac{PT^2 + QU^2 + RV^2 + SW^2}{PQ^2 + PR^2 + PT^2}.\]

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