
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
Given a convex quadrilateral \(ABCD\) with side \(AD\) equal to 3. The diagonals \(AC\) and \(BD\) intersect at point \(E\), and it is known that the areas of triangles \(ABE\) and \(DCE\) are both equal to 1. Find the side \(BC\), given that the area of \(ABCD\) does not exceed 4.

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