
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 removed from the log by making two planar cuts, one perpendicular to the axis of the cylinder, and the other at a $30^\circ$ angle with the plane of the first cut. The intersection of these planes touches the log at exactly one point. Express the number of cubic inches in the wedge in the form $m\pi$, where $m$ is a positive integer, and determine $m$.

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