
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 a circle with area $A_1$ contained in the interior of a larger circle with area $A_1+A_2$, where the radius of the larger circle is $3$, and $A_1, A_2, A_1 + A_2$ is an arithmetic progression, find the radius of the smaller circle.

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