
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 that go entirely through the log. 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 has exactly one point in common with the log. Calculate the volume of the wedge in cubic inches, expressed as $n\pi$, where $n$ is a positive number.

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