
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 \( A B C \), points \( M \) and \( N \) are chosen on sides \( A B \) and \( B C \) respectively such that \( A M = 2 M B \) and \( B N = N C \). Segments \( A N \) and \( C M \) intersect at point \( P \). Find the area of quadrilateral \( M B N P \) if it is known that the area of triangle \( A B C \) is 30.

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