
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
In triangle \( \triangle ABC \), the points \( M \) and \( N \) trisect \( AC \), and the points \( X \) and \( Y \) trisect \( BC \). Lines \( AY \) and \( BM, BN \) intersect at points \( S \) and \( R \), respectively. Find the ratio of the area of quadrilateral \( SRNM \) to the area of \( \triangle ABC \).

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