
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. Two planar cuts are made through the entire log. The first cut is perpendicular to the axis of the cylinder, and the second cut's plane forms a $60^\circ$ angle with that of the first cut. The intersection of these two planes touches the log at exactly one point. Calculate the volume of the wedge formed, expressed as $m\pi$, where $m$ is a positive integer.

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