
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 $ABC,$ point $D$ is on $\overline{AB}$ such that $AD:DB = 2:1,$ and point $E$ is on $\overline{BC}$ such that $BE:EC = 2:1.$ Lines $DE$ and $AC$ intersect at point $F.$ Determine the ratio $\frac{DE}{EF}.$

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