
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 that all vertices of the tetrahedron $A-BCD$ are on the surface of sphere $O$, and $AB$ is the diameter of sphere $O$, if the volume of the tetrahedron is $\frac{4\sqrt{3}}{3}$, $BC=4$, $BD=\sqrt{3}$, and $\angle CBD=90^{\circ}$, calculate the surface area of sphere $O$.

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