
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 \( \triangle ABC \), \( AB = 12 \), \( AC = 16 \), \( M \) is the midpoint of \( BC \), \( E \) and \( F \) are points on \( AB \) and \( AC \) respectively. \( EF \) intersects \( AM \) at \( G \), and \( AE = 2AF \). Find the ratio \( \frac{EF}{GF} \).

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