
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 the arrangement of two concentric circles, the radius of the outer circle is three times the radius of the inner circle. Calculate the area of the space between the two circles (the gray region) if the width of this region is 4 feet. Express your answer in terms of $\pi$.

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