
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 $AB = 15$ on a straight line with points $C$ and $D$ lying on the same side of line $AB$ such that $\triangle ABC$ is congruent to $\triangle DAB$. Both $BC$ and $AD$ measure 13, and $CA$ and $DB$ both measure 18. Points $E$ and $F$ are defined on $BC$ and $AD$, respectively, such that $BE = AF = 3$. Find the area of the intersection of triangles $ABE$ and $ADF$ (denoted as quadrilateral $AEFD$).

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