
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 two parallel lines \(A B\) and \(C D\) with a distance \(b\) between them. There are two points: \(M\) on \(A B\) and \(N\) on \(C D\). A segment \(M E = a\) is marked on \(A B\) from point \(M\). Which point \(L\) on the line \(M N\) should be connected to the point \(E\) so that the sum of the areas of triangles \(E L M\) and \(N L F\) is minimized? Here, \(F\) is the point of intersection of the line \(E L\) with \(C D\).

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