
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 triangle \( ABC \), \( N \) is the midpoint of \( \overline{AC} \), \( AB = 10 \), and \( BC = 18 \). Let \( D \) be on \( \overline{BC} \), and \( E \) be on \( \overline{AB} \), and let \( F \) be the intersection of \( \overline{DE} \) and \( \overline{AN} \). If \( BD = 3BE \), find \( \frac{DF}{FE} \).

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