
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 plane intersects the edges of a tetrahedron \(A B C D\) that originate from vertex \(C\) and divides them in the ratio \(4:1\) (not necessarily from vertex \(C\)). Additionally, this plane intersects the lines \(AB\) and \(BD\) at points \(E\) and \(F\). Find the ratio of the areas of triangles \(B E F\) and \(A B D\).

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