
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 tetrahedron $ABC D$ that emanate from vertex $A$ and divides them in the ratio $3:1$ (not necessarily from vertex $A$). Additionally, this plane intersects the lines $BC$ and $CD$ at points $E$ and $F$, respectively. Find the ratio of the areas of triangles $EFC$ and $BCD$.

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