
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 $BE:EC = 2:3$. If lines $DE$ and $AC$ intersect at $F$, then find the value of $\frac{DE}{EF}$.

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