
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 4-dimensional hyperparallelepiped $ABCDEFGHJKLMN$ is generated by vectors $\overrightarrow{AB},$ $\overrightarrow{AD},$ $\overrightarrow{AE},$ and $\overrightarrow{AF},$ with $A$ at the origin. Compute
\[
\frac{AG^2 + BK^2 + CM^2 + DN^2}{AB^2 + AD^2 + AE^2 + AF^2}.
\]

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