
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 triangle \( ABC \), the medians \( \overline{AD} \) and \( \overline{CE} \) measure \( 20 \) and \( 30 \), respectively, and \( AB = 28 \). Extend \( \overline{CE} \) to meet the circumcircle of \( ABC \) at point \( F \). Find the area of triangle \( AFB \) in the form \( p\sqrt{q} \), where \( p \) and \( q \) are positive integers and \( q \) is not divisible by the square of any prime. Compute \( p+q \).

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