
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
Given quadrilateral \(ABCD\) with an area of 45, diagonals \(AC\) and \(BD\) intersect at point \(P\). Points \(M\) and \(N\) are located on sides \(AB\) and \(CD\) respectively such that \(MB = \frac{1}{3} AB\), \(BP = \frac{3}{5} BD\), \(NC = \frac{2}{3} DC\), and \(PC = \frac{2}{3} AC\). Find the area of quadrilateral \(MBCN\).

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