
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
The height of a cone is divided into three equal segments, and planes parallel to the base are drawn through the points of division, splitting the cone into three parts. Find the volume of the middle truncated cone if the volume of the given cone is \( V \).

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