
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
In the triangle shown below, with vertices $A$, $B$, and $C$, lines $\overline{CD}$, $\overline{AE}$, and $\overline{BF}$ are half of their respective sides. It follows that $\overline{AN_2}: \overline{N_2N_1}: \overline{N_1D} = 2: 1: 2$, and similarly for lines $\overline{BE}$ and $\overline{CF}$. Calculate the area of triangle $N_1N_2N_3$ as a fraction of $\triangle ABC$.

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