
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
The diagonals of the parallelogram \(ABCD\) intersect at \(E\). The bisectors of \(\angle DAE\) and \(\angle EBC\) intersect at \(F\). Assume that \(ECFD\) is a parallelogram. Determine the ratio \(AB : AD\).

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