
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 a convex quadrilateral \(ABCD\), \(\angle BAC = \angle CAD\) and \(\angle ABC = \angle ACD\). The extensions of \(AD\) and \(BC\) meet at \(E\), and the extensions of \(AB\) and \(DC\) meet at \(F\). Determine the value of 
\[
\frac{AB \cdot DE}{BC \cdot CE}.
\]

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