
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 a convex quadrilateral \(ABCD\) with parallel sides \(AD\) and \(BC\), a line \(L\) is drawn parallel to \(AD\) and intersects sides \(AB\) and \(CD\) at points \(M\) and \(N\), respectively. It is known that quadrilaterals \(AMND\) and \(MBNS\) are similar, and the sum of the lengths of sides \(AD\) and \(BC\) is no more than 4. Find the maximum possible length of segment \(MN\).

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