
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 segment \( AD \) is the bisector of the right triangle \( ABC \) (\(\angle C=90^{\circ}\)). A circle with radius \(\sqrt{15}\) passes through points \( A, C, D \) and intersects side \( AB \) at point \( E \) such that \( AE: AB = 3: 5 \). Find the area of triangle \( ABC \).

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