
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 radius 10 units, two parallel chords $CD$ and $EF$ are 12 units and 16 units long, respectively. Chord $EF$ is closer to the center $O$ than $CD$. If point $K$ is on the diameter that extends through $O$ and $A$, where $A$ is the end point of the diameter opposite to $K$, and $KA = 20$ units, find the area of triangle $KDC$.

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