
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
Consider a triangular pyramid with a triangular base where all sides are equal (\(\Delta ABC\)). The side length of the base triangle is \(s\). There are two additional triangular faces, \(\Delta ADE\) and \(\Delta BCF\), joined at a vertex \(G\), and each side of these triangles also measures \(s\). Given \(s = 6\sqrt{3}\), calculate the volume of the original pyramid.

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