
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
Two different points, $C$ and $D$, lie on the same side of line $AB$ which forms the common base of two congruent triangles $\triangle ABC$ and $\triangle BAD$. Here $AB = 12$, $BC = AD = 15$, and $CA = DB = 20$. An additional line segment $EF$ intersects line segment $AB$ at its midpoint $M$ and meets $CD$ at a right angle at point $N$. If $CN = 8$, find the area of intersection between $\triangle ABC$ and $\triangle BAEF$.

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