
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

	 Let  $ABC$  be a triangle such that  $AB = 13$ ,  $BC = 14$ ,  $CA = 15$  and let  $E$ ,  $F$  be the feet of the altitudes from  $B$  and  $C$ , respectively.
Let the circumcircle of triangle  $AEF$  be  $\omega$ .
We draw three lines, tangent to the circumcircle of triangle  $AEF$  at  $A$ ,  $E$ , and  $F$ .
Compute the area of the triangle these three lines determine.

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