
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 an area of \( A_{1} \) contained within a larger circle with an area of \( A_{1} + A_{2} \), where the radius of the larger circle is 3 and \( A_{1}, A_{2}, A_{1}+A_{2} \) form an arithmetic sequence, calculate the radius of the smaller circle.

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