
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 $ABCDEFGH$ is formed by vectors $\overrightarrow{AB}, \overrightarrow{AD},$ and $\overrightarrow{AE},$ where $\overrightarrow{AE}$ is scaled by a factor $\alpha \neq 1$. Calculate:
\[
\frac{AG^2 + BH^2 + CE^2 + DF^2}{AB^2 + AD^2 + AE^2}.
\]

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