
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 $ABC$, $M$ is the midpoint of $\overline{BC}$, $AB = 15$, and $AC = 18$. Let $E$ be on $\overline{AC}$, and $F$ be on $\overline{AB}$, and let $G$ be the intersection of $\overline{EF}$ and $\overline{AM}$. If $AE = 3AF$, then find $\frac{EG}{GF}$.

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