
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 a regular hexagon where each side length is 12 cm, an equilateral triangle is inscribed such that one vertex of the triangle is a vertex of the hexagon and the two other vertices of the triangle bisect the opposite sides of the hexagon. Calculate the area of the triangle created by the intersection of the equilateral triangle and the hexagon.

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