
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 $\angle ABC = 100^\circ, AB = 20$, and $BC = 12$. Extend $\overline{CD}$ through $D$ to $E$ so that $DE = 6$. If $\overline{BE}$ intersects $\overline{AD}$ at $F$, then find the length of $FD$.
A) 1.5
B) 2.3
C) 2.8
D) 3.1
E) 3.5

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