
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 right trapezoid \( ABCD \), it is known that \(\angle A = \angle D = 90^\circ\), \(DE \perp AC\) at point \(E\), \(\angle ACD = \angle EBC = 30^\circ\), and \(AD = \sqrt{3}\). Find \(BC\).

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