
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
A certain artifact is formed by removing a cone from a regular triangular prism. The edges of the regular triangular prism ABC-A₁B₁C₁ are all 2 units in length. The vertex of the cone is at the center of triangle ABC, and its base is the incircle of triangle A₁B₁C₁. Calculate the volume of this artifact.

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