
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 height of a truncated cone is equal to the radius of its larger base; the perimeter of a regular hexagon inscribed in the smaller base is equal to the perimeter of an equilateral triangle inscribed in the larger base. Determine the angle of inclination of the cone's generatrix to the plane of the base.

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