
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
The diagram below shows a shaded region bounded by two concentric circles where the outer circle has twice the radius of the inner circle. The total boundary of the shaded region has length  $36\pi$ . Find  $n$  such that the area of the shaded region is  $n\pi$ .
![Image](https://cdn.artofproblemsolving.com/attachments/4/5/c9ffdc41c633cc61127ef585a45ee5e6c0f88d.png)

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