
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 triangle ABC, point $D$ is on segment $AC$ such that $AD = DC$, and point $E$ is on segment $AB$ such that $AE = EB$. If segment $CE$ intersects segment $BD$ at point $F$, and the measure of $\angle BFC = x$, find the ratio of the measure of $\angle BFC$ to the measure of $\angle BDF$.

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