
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
Point \( O \) is the center of an ellipse with major axis \( \overline{AB} \) and minor axis \( \overline{CD} \). Point \( F \) is one focus of the ellipse. If \( OF = 8 \) and the diameter of the inscribed circle of triangle \( OCF \) is 4, compute the product \( (AB)(CD) \).

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