
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}$  have lengths 18 and 27, respectively, and  $ AB \equal{} 24$ .  Extend  $ \overline{CE}$  to intersect the circumcircle of  $ ABC$  at  $ F$ .  The area of triangle  $ AFB$  is  $ m\sqrt {n}$ , where  $ m$  and  $ n$  are positive integers and  $ n$  is not divisible by the square of any prime.  Find  $ m \plus{} n$ .

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