
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
In the isosceles trapezoid \( ABCD \) where \( AB \parallel CD \) and \( AB > CD \), let the eccentricity of the hyperbola with foci at \( A \) and \( B \) passing through point \( D \) be \( e_1 \), and the eccentricity of the ellipse with foci at \( C \) and \( D \) passing through point \( A \) be \( e_2 \). What is \( e_1 e_2 \)?

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