
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 cone and a hemisphere share the same base. If the volume of the cone is exactly equal to the volume of the hemisphere, then the cosine of the apex angle of the cone's axial section is ______.

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