
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
Let \(ABCD\) be a trapezoid with \(AB \parallel CD\) and \(\angle D = 90^\circ\). Suppose that there is a point \(E\) on \(CD\) such that \(AE = BE\) and that triangles \(AED\) and \(CEB\) are similar, but not congruent. Given that \(\frac{CD}{AB} = 2014\), find \(\frac{BC}{AD}\).

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