
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 a cuboid has all its vertices on the surface of a sphere, and the lengths of the three edges emanating from the same vertex of the cuboid are \(1\), \(2\), and \(3\), respectively, determine the surface area of this sphere.

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