
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 sphere $O$ with radius $R$, a section is made through the midpoint of a radius of sphere $O$ and perpendicular to this radius. The area of this section is $3\pi$. If a right square prism has a base that is a square with side length $1$ and all eight vertices are on the surface of sphere $O$, then the surface area of this prism is $\boxed{4\sqrt{14}+2}$.

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