
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 plane passing through the vertex of a cone intersects the base along a chord, the length of which is equal to the radius of the base. Determine the ratio of the volumes of the resulting parts of the cone.

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