
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
The solid shown has a square base of side length $s$. Each side of the square base is extended downwards at an angle, meeting at a point directly below the center of the base, forming an inverted pyramid. The height of this point below the base is equal to the side length $s$. Given that \( s = 4\sqrt{3} \), calculate the volume of this inverted pyramid.

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