
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
A repair crew needs to walk to the center \(C\) of a circular fountain. They place a 24-foot plank from \(A\) to \(B\) and then a 14-foot plank from \(D\) to \(C\), where \(D\) is one-third of the way along \(\overline{AB}\) from \(A\) to \(B\). Calculate the area of the circular base of the fountain. Express your answer in terms of \(\pi\).

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