
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 sphere is inscribed in a truncated cone. The sum of the lengths of the diameters of the upper and lower bases of the cone is five times the length of the radius of the sphere. Find the angle between the slant height of the cone and the plane of the base.

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