
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 rectangle \(ABCD\), \(E\) and \(F\) are chosen on \(\overline{AB}\) and \(\overline{CD}\), respectively, so that \(AEFD\) is a square. If \(\frac{AB}{BE} = \frac{BE}{BC}\), determine the value of \(\frac{AB}{BC}\).

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