
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
The height of trapezoid \(ABCD\) is 7, and the bases \(AD\) and \(BC\) are 8 and 6, respectively. A line \(BE\) is drawn through point \(E\) on side \(CD\), dividing diagonal \(AC\) at point \(O\) in the ratio \(AO : OC = 3 : 2\). Find the area of triangle \(OEC\).

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