
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
Let $ABCD$ be a parallelogram with $\angle ABC = 100^\circ, AB = 12$ and $BC = 8$. Extend line $\overline{CD}$ through $D$ to $E$ such that $DE = 4$. If line segment $\overline{BE}$ intersects line segment $\overline{AD}$ at $F$, find the closest value of $FD$.
A) $2$
B) $3$
C) $4$
D) $5$

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