
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 lateral sides \( AB \) and \( CD \) of trapezoid \( ABCD \) are 8 and 10 respectively, and the base \( BC \) is 2. The angle bisector of \(\angle ADC\) passes through the midpoint of the side \( AB \). Find the area of the trapezoid.

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