
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
We draw $n$ circles between the sides of an angle $\alpha$, where each circle touches both sides of the angle, and (except for the smallest and largest circles) each circle touches two neighboring circles. What is the sum of the areas of these $n$ circles if the radius of the smallest circle is $r_{1}$?

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