
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 \(ABCD\), the side \(AB\) is perpendicular to both \(AD\) and \(BC\), and \(|AB|=\sqrt{|AD| \cdot |BC|}\). Let \(E\) be the point where the non-parallel sides intersect, \(O\) be the point where the diagonals intersect, and \(M\) be the midpoint of \(AB\). Find \(\angle EOM\).

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