
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 triangle \(ABC\), the sides are known: \(AB = 6\), \(BC = 4\), and \(AC = 8\). The angle bisector of \(\angle C\) intersects side \(AB\) at point \(D\). A circle is drawn through points \(A\), \(D\), and \(C\), intersecting side \(BC\) at point \(E\). Find the area of triangle \(ADE\).

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