
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 a general triangle $ABC$, points $D, E, F$ are defined as follows:

- Point $D$ divides segment $AB$ in the ratio $1:2$, closer to point $A$.
- Point $E$ divides segment $BC$ in the ratio $1:2$, closer to point $B$.
- Point $F$ divides segment $CA$ in the ratio $1:2$, closer to point $C$.

Determine the ratio of the areas of triangles $ABC$ and $DEF$.

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