
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
On the sides \(AB, BC, CD,\) and \(DA\) of parallelogram \(ABCD\), points \(M, N, K,\) and \(L\) are taken, respectively, such that \(AM : MB = CK : KD = 1 : 2\) and \(BN : NC = DL : LA = 1 : 3\). Find the area of the quadrilateral whose vertices are the intersections of the segments \(AN, BK, CL,\) and \(DM\), given that the area of parallelogram \(ABCD\) is 1.

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