
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
Let $A B C D$ be a tetrahedron with volume $V$. Point $E$ is the midpoint of edge $A D$, and point $F$ is on the extension of $A B$ such that $B F = A B$. The plane passing through points $C$, $E$, and $F$ intersects $B D$ at point $G$. Determine the volume of the tetrahedron $C D G E$.

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