
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
Two concentric circles have the radius of the inner circle as \( r \) feet and the outer circle as \( 3r \) feet. If the width of the gray region between these circles is \( 4 \) feet, what is the area of the gray region, expressed in terms of \( \pi \) and \( r \)?

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