
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
Given a circle with center \(O\) and radius \(OD\) perpendicular to chord \(AB\), intersecting \(AB\) at point \(C\). Line segment \(AO\) is extended to intersect the circle at point \(E\). If \(AB = 8\) and \(CD = 2\), calculate the area of \(\triangle BCE\).

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