
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

In a triangular prism \(ABC A_1 B_1 C_1\), two planes are drawn: one passing through the vertices \(A, B\), and \(C_1\), and the other passing through the vertices \(A_1, B_1\), and \(C\). These planes divide the prism into four parts. The volume of the smallest of these parts is \(V\). Find the volume of the prism.

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