
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
If the three edges connected to a vertex of a rectangular parallelepiped are 1, 2, and 2, respectively, and all eight vertices of the parallelepiped lie on the same sphere, calculate the surface area of the sphere.

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