
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 $ABC$, let segments $\overline{CD}$, $\overline{AE}$ and $\overline{BF}$ each be one-fourth the length of their respective sides ($\overline{AB}$, $\overline{BC}$, and $\overline{CA}$). The points $D$, $E$, and $F$ divide their respective sides such that $\overline{CD} = \frac{1}{4}\overline{BC}$, $\overline{AE} = \frac{1}{4}\overline{AB}$, and $\overline{BF} = \frac{1}{4}\overline{CA}$. Determine the area of triangle $N_1N_2N_3$, formed by the intersection points $N_1$, $N_2$, and $N_3$ of lines $AD$, $BE$, and $CF$ respectively.

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