
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 parallelogram $ABCD$, side $AB = 420$. Point $E$ is taken on side $BC$ such that $BE: EC = 5: 7$, and line $DE$ is drawn intersecting the extension of $AB$ at point $F$. Find $BF$.

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