
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 \(ABCD\), points \(K\) and \(M\) are the midpoints of the bases \(AB\) and \(CD\), respectively. It is known that \(AM\) is perpendicular to \(DK\) and \(CK\) is perpendicular to \(BM\), and the angle \(CKD\) is equal to \(60^\circ\). Find the area of the trapezoid if its height is 1.

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