
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 \( SABC \), \(\triangle ABC\) is an equilateral triangle. The projection of point \( A \) onto the plane \( SBC \), denoted as \( H \), is the orthocenter of \(\triangle SBC\). The dihedral angle \( \angle H-ABC \) is \( 30^\circ \). Given that \( SA = 2\sqrt{3} \), find the volume of the tetrahedron \( SABC \).

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