
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 \(AD\) is perpendicular to the bases and is equal to 9. \(CD\) is 12, and the segment \(AO\), where \(O\) is the point of intersection of the diagonals of the trapezoid, is equal to 6. Find the area of triangle \(BOC\).

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