
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
As shown in the diagram, \( F \) is a fixed point, \( l \) is a fixed line, and the distance from point \( F \) to line \( l \) is \( p \). Point \( M \) slides along line \( l \), and moving point \( N \) is on the extension of \( M F \), satisfying the condition 
\[
\frac{|F N|}{|M N|} = \frac{1}{|M F|}.
\]
Find the locus of the moving point \( N \).

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