
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 trapezoid \(ABCD\), \(AD\) is parallel to \(BC\). \(\angle A = \angle D = 45^\circ\), while \(\angle B = \angle C = 135^\circ\). If \(AB = 6\) and the area of \(ABCD\) is 30, find \(BC\).

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