
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 smaller base \(BC\) is equal to 3, and the legs \(AB\) and \(CD\) are each equal to 3. The diagonals of the trapezoid form an angle of \(60^\circ\) with each other. Find the base \(AD\).

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