
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 diagram, circle \(P\) has a radius of 10 units. Chord \(EF\) has a length of 12 units and is parallel to segment \(LM\). If \(LN = 20\) units and points \(L\), \(N\), \(P\), and \(M\) are collinear, what is the area of triangle \(LEF\)?

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