
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 \(O\) has a radius of 10 units. Chord \(EF\) has a length of 12 units and is parallel to segment \(LB\). Given that \(LA\) = 20 units and points \(L\), \(A\), \(O\), and \(B\) are collinear, what is the area of triangle \(LEF\)? Assume \(E\) and \(F\) are above line \(AB\) and \(LE\) and \(LF\) are segments connecting \(L\) to points on the circle.

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