
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
In the right prism $ABC-A_{1}B_{1}C_{1}$, all six vertices are on the surface of a sphere $O$. Given $AC=1$, $BC=3$, $\angle ACB=60^{\circ}$, and $C_{1}C=2\sqrt{3}$, calculate the surface area of sphere $O$.

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