
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]


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Inside a unit cube \( ABCD-A'B'C'D' \), there is an inscribed sphere \( O \). Additionally, a small sphere is placed at each of the eight corners of the cube, such that each small sphere is externally tangent to the inscribed sphere and tangents three faces of the cube. What is the radius of each small sphere?

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