
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 perpendicular dropped from the center of the base of a cone onto its slant height rotates about the cone's axis. Find the angle between its slant height and the axis if the surface of rotation divides the cone's volume in half.

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