
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 prism $ABC-A_1B_1C_1$ with the lateral edges perpendicular to the base and all vertices lying on the same spherical surface, and given the volume of the prism is $\sqrt{3}$, the length of $AB$ is $2$, the length of $AC$ is $1$, and the measure of $\angle BAC$ is $60°$, find the surface area of this sphere.

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