
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, with the height of the cylinder equal to the diameter of the cone's base. The total surface area of the cylinder is equal to the area of the base of the cone. Find the angle between the generatrix (slant height) of the cone and the plane of its base.

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