
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 \(ABC\), \(D\) is on \(\overline{AB}\) such that \(AD:DB = 2:3\), and \(E\) is on \(\overline{BC}\) such that \(BE:EC = 4:1\). If lines \(DE\) and \(AC\) intersect at \(F\), then find \(\frac{DE}{EF}\).

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