
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 reach the center \( C \) of a circular fountain for maintenance, a crew uses a 20-foot plank from point \( A \) to point \( B \) and then a 12-foot plank from point \( D \) to \( C \), where \( D \) is the midpoint of \( \overline{AB} \). Determine the area of the circular base of the fountain in terms of \(\pi\).

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