
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 right triangular pyramid with pairwise perpendicular edges, its three side faces have areas of 4, 6, and 12 square units. Calculate the surface area of the circumscribing sphere.

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