
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 trapezoid \(ABCD\), the side \(AB\) is equal to the base \(BC\), and the angle \(BAD\) is \(60^\circ\). The diagonal \(BD\) is equal to 3.

The area of triangle \(ACD\) is to the area of triangle \(ABC\) as \(2:1\). Find all the sides of trapezoid \(ABCD\).

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