
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
The two concentric circles have the same center $O$. A chord $\overline{EF}$ of the larger circle is tangent to the smaller circle at point $G$. The distance from $O$ to $F$ is $12$ units, and the length of chord $\overline{EF}$ is $20$ units. Find the area between the two circles.

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