
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
The diameter \( AB \) of a circle of radius \( 3 \) is extended to a point \( D \) outside the circle such that \( BD = 4 \). Point \( E \) is chosen such that \( ED = 6 \) and line \( ED \) makes an angle of 30 degrees with line \( AD \). The segment \( AE \) intersects the circle at a point \( C \) between \( A \) and \( E \). Determine the area of triangle \( ABC \).

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