
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 cylinder is inscribed in a cone, whose axial cross-section is a right triangle, with its lower base lying in the plane of the cone's base. The ratio of the lateral surfaces of the cone and the cylinder is equal to \(4 \sqrt{2}\). Find the angle between the plane of the cone's base and a line passing through the center of the upper base of the cylinder and an arbitrary point on the circumference of the cone's base.

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