
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 triangular prism \( ABC A_1 B_1 C_1 \) with the base \( ABC \) and lateral edges \( AA_1, BB_1, CC_1 \) is intersected by a plane passing through points \( E, F, C \), where point \( E \) is the midpoint of edge \( AA_1 \), and point \( F \) lies on edge \( BB_1 \) such that \( BF:FB_1 = 1:2 \). Find the volume of the part of the prism \( ABC A_1 B_1 C_1 \) that is enclosed between the intersecting plane and the base of this prism, given that the volume of the prism is \( V \).

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