
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 3, compute the product $(AB)(CD)$.

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