
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 cylindrical log has a diameter of $16$ inches. A wedge is cut from the log by making two planar cuts. The first cut is perpendicular to the axis of the cylinder, and the plane of the second cut forms a $60^\circ$ angle with the plane of the first cut. The intersection of these two planes touches the log at exactly one point. Determine the volume of the wedge, expressed as $m\pi$, where $m$ is a positive integer.

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