
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 five pieces by planes parallel to its base. All of these pieces have the same height. What is the ratio of the volume of the third-largest piece to the volume of the largest piece?

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