
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 three pieces by planes parallel to its base, each piece having equal height. The pieces are labeled from top to bottom; hence the smallest piece is at the top and the largest at the bottom. Calculate the ratio of the volume of the smallest piece to the volume of the largest piece.

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