
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 slant height of a cone forms an angle $\alpha$ with the plane of its base, where $\cos \alpha = \frac{1}{4}$. A sphere is inscribed in the cone, and a plane is drawn through the circle of tangency of the sphere and the lateral surface of the cone. The volume of the part of the cone enclosed between this plane and the base plane of the cone is 37. Find the volume of the remaining part of the cone.

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