
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 an isosceles triangle \(ABC\), it is known that \(AC = 4\) and \(AB = BC = 6\). The angle bisector of \(\angle C\) intersects side \(AB\) at point \(D\). A circle is drawn through point \(D\), touching side \(AC\) at its midpoint, and intersects the segment \(AD\) at point \(E\). Find the area of the triangle \(DEC\).

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