
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 that points \(D\), \(E\), and \(F\) are on the sides \(BC\), \(CA\), and \(AB\) of triangle \( \triangle ABC \) respectively, such that \(AF:FB = BD:DC = CE:EA = 1:m\). Let \(AD \cap BE = N\), \(BE \cap CF = M\), \(CF \cap AD = P\). Find the ratio of the area of \( \triangle MNP \) to the area of \( \triangle ABC \).

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