
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]


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Each lateral face of a triangular prism is perpendicular to the base, the base is an equilateral triangle, and the ratio of the lateral edge length to the base side length is 2:1. All vertices are on the surface of a sphere. If the surface area of the sphere is $\frac{16}{3}\pi$, calculate the lateral surface area of this triangular prism.

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