
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 tetrahedron \( D-ABC \) shown in the diagram, it is known that \( DA \) is perpendicular to the plane \( ABC \), and \( \triangle ABC \) is an equilateral triangle with side length 2. When the tangent value of the dihedral angle \( A-BD-C \) is 2, the volume \( V \) of the tetrahedron \( D-ABC \) is \(\qquad\)

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