
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 points \( K, L, M \), and \( N \) are the midpoints of the sides \( AB, BC, CD, \) and \( AD \) respectively of a parallelogram \( ABCD \) with area \( s \). Find the area of the quadrilateral formed by the intersection of the lines \( AL, AM, CK, \) and \( CN \).

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