
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
A smaller circle is enclosed within a larger circle. The larger circle has a radius of 5 units. The areas of the smaller and larger circles maintain the relation where \( A_1 \), \( A_2 \), and \( A_1 + A_2 \) (with \( A_1 \) being the area of the smaller circle and \( A_2 \) the area difference between the two circles) form an arithmetic progression. Evaluate the radius of the smaller circle assuming the areas are proportional to the aforementioned arithmetic sequence.

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