
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
Given that the volume of tetrahedron \(ABCD\) is \(V\), point \(E\) is the midpoint of edge \(AD\), point \(F\) lies on the extension of \(AB\) such that \(BF = AB\). The plane passing through points \(C\), \(E\), and \(F\) intersects \(BD\) at point \(G\). Determine the volume of tetrahedron \(CDGE\).

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