
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
Consider a circle of radius \( R \) centered at the origin on the Cartesian plane. Specify at least one value of \( R \) for which there are exactly 32 integer points (a point is called an integer point if both its x-coordinate and y-coordinate are integers) lying on this circle.

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