
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 an isosceles trapezoid \(ABCD\), \(AB\) is parallel to \(CD\) and \(AB > CD\). Define a hyperbola with foci at \(A\) and \(B\) that passes through point \(D\), and an ellipse with foci at \(C\) and \(D\) that passes through point \(A\). Let the eccentricities of the hyperbola and the ellipse be \(e_1\) and \(e_2\) respectively. Find the value of \(e_1 e_2\).

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