
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 the trapezoid \(MPQF\), the bases are \(MF = 24\) and \(PQ = 4\). The height of the trapezoid is 5. Point \(N\) divides the side into segments \(MN\) and \(NP\) such that \(MN = 3NP\).

Find the area of triangle \(NQF\).

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