
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 the curve \( x^{2 / 3} + y^{2 / 3} = 1 \), when it intersects with a circle centered at the origin with radius \( r \), it is found that the 8 intersection points can be grouped such that the sides of two resulting squares are tangent to the curve \( g \), with each side being tangent exactly at one of their endpoints. What is the radius \( r \)?

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