
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 diagonals of a convex quadrilateral \(ABCD\) intersect at point \(E\). It is known that the area of each of the triangles \(ABE\) and \(DCE\) is equal to 1, and the area of the entire quadrilateral does not exceed 4. Given that \(AD = 3\), find the side \(BC\).

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