
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
Given that a smaller circle is entirely inside a larger circle, such that the larger circle has a radius $R = 2$, and the areas of the two circles form an arithmetic progression, with the largest area being that of the larger circle, find the radius of the smaller circle.

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