
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 \( \triangle ABC \) be a right triangle with \( \angle A = 90^\circ \). Let \( D \) be the midpoint of \( AB \) and let \( E \) be a point on segment \( AC \) such that \( AD = AE \). Let \( BE \) meet \( CD \) at \( F \). If \( \angle BFC = 135^\circ \), determine \( \frac{BC}{AB} \).

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