
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 base \( AB \) of trapezoid \( ABCD \) is twice the base \( CD \) and twice the leg \( AD \). Diagonal \( AC \) is equal to \( a \), and leg \( BC \) is equal to \( b \). Find the area of the trapezoid.

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