
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
Inside a cube \( C \) with side length 1, an inscribed sphere \( O_{1} \) is placed. Another sphere \( O_{2} \) is also placed inside \( C \) such that it is tangent to the inscribed sphere \( O_{1} \) and also tangent to three faces of the cube. What is the surface area of sphere \( O_{2} \)?

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