
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
We draw four non-intersecting circles inside a square. Each circle touches two sides of the square and exactly two of the circles, where the radii of the circles are equal. What can be the radii of the circles?

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