
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 \( BC \) and \( AC \) of triangle \( ABC \), points \( M \) and \( N \) are taken respectively such that \( CM:MB = 1:3 \) and \( AN:NC = 3:2 \). Segments \( AM \) and \( BN \) intersect at point \( K \). Find the area of quadrilateral \( CMKN \), given that the area of triangle \( ABC \) is 1.

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