
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 the triangle $ABC$, points $D$, $E$, and $F$ are on segments $AB$, $BC$, and $CA$, respectively. $D$ is located so that $\angle ADE = 50^\circ$ and $\angle DEF = 30^\circ$. If $\angle EDF = 40^\circ$, what is the measure of $\angle BDF$ in degrees?

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