
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
Let \( ABC \) be an isosceles triangle with \( AB = AC \). Let \( D \) and \( E \) be the midpoints of segments \( AB \) and \( AC \), respectively. Suppose that there exists a point \( F \) on ray \( \overrightarrow{DE} \) outside of \( ABC \) such that triangle \( BFA \) is similar to triangle \( ABC \). Compute \( \frac{AB}{BC} \).

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