
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 given circle $O$ with radius 10 units, chord $EF$ has length 10 units and is parallel to the diameter $LM$. If $LZ$ = 20 units and points $L$, $M$, $O$, and $Z$ are collinear, calculate the area of triangle $LEF$. Create a geometrical sketch to assist visualization.

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