
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
Point \( K \) lies on side \( BC \) of parallelogram \( ABCD \), and point \( M \) lies on its side \( AD \). Segments \( CM \) and \( DK \) intersect at point \( L \), and segments \( AK \) and \( BM \) intersect at point \( N \). Find the maximum value of the ratio of the areas of quadrilateral \( KLMN \) to \( ABCD \).

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