
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 \(ABC\), points \(M\) and \(N\) are selected on sides \(AB\) and \(BC\) respectively such that \(AM = 2MB\) and \(BN = NC\). The segments \(AN\) and \(CM\) intersect at point \(P\). Find the area of quadrilateral \(MBNP\), given that the area of triangle \(ABC\) is 30.

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