
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  $\tfrac{CD}{AB}=2014$ , find  $\tfrac{BC}{AD}$ .

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