
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 with edge length 1, an inscribed sphere \( O_1 \) is drawn. Another smaller sphere \( O_2 \) is drawn inside the cube such that it is externally tangent to the larger sphere and simultaneously tangent to three faces of the cube. What is the surface area of the smaller sphere \( O_2 \)?

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