
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
To access a water valve at the center $C$ of a round garden, a gardening team positions a 20-foot board from $A$ to $B$, and then a 15-foot board from $D$ to $C$, where $D$ is one-third of the way along $\overline{AB}$ from $A$ to $B$. Determine the area of the circular garden. Express your answer in terms of $\pi$.

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