
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

On the extension of side \( AB \) beyond point \( B \) of triangle \( ABC \), segment \( AD \) is laid out such that \( AD:AB = \alpha \). On the extension of median \( BE \), segment \( EF \) is laid out so that \( EF:BE = \beta \). Find the ratio of the areas of triangles \( BDF \) and \( ABC \).

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