
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
A rectangular prism has one vertex where the lengths of the three edges are $3$, $4$, and $5$, respectively. Additionally, all eight vertices of the prism are on the same sphere. What is the surface area of this sphere?

A) $20 \sqrt{2}\pi$
B) $25 \sqrt{2}\pi$
C) $50\pi$
D) $200\pi$

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