
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 a circle with center $O$ and a radius of 10 units, chord $EF$ has a length of 12 units and is parallel to diameter $GH$. Point $J$, outside the circle, is on line $GH$, such that $HJ = 20$ units and points $J, H, O, G$ are collinear. Determine the area of triangle $JEF$.

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