
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 right circular cone is sliced into four parts by three vertical cuts through the apex, splitting the cone into four equal angular sectors. Each slice goes from the apex down to the base and equally subdivides the circular base. Find the ratio of the volume of the largest resulting sector to that of the second largest.

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