
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
Given an equilateral $\triangle ABC$ with side length $2$ and point $D$ on ray $\overrightarrow{BC}$ such that $CD = 4$, find $\tfrac{AE}{AF}$, where $E$ and $F$ lie on $\overline{AB}$ and $\overline{AC}$, respectively, and the area of $\triangle AEF$ is half of the area of $\triangle ABC$.

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