
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
We intersect a right circular cone, which has a base diameter of \(26 \, \text{cm}\) and a height of \(39 \, \text{cm}\), with a plane that shares only one point with the base circle and intersects the cone's axis at a distance of \(30 \, \text{cm}\) from the apex. Determine the volume ratio of the two resulting parts.

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