
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
Several circles are inscribed in a corner, and their radii increase such that each subsequent circle touches the previous one. Find the sum of the circumferences of the second and fourth circles, given that the circumference of the third circle is \(18 \pi\), and the area of the circle bounded by the first circle is \(\pi\).

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