
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 $\overline{BC}$ through $C$ to point $E$ such that $CE = 6$. If $\overline{AE}$ intersects $BD$ at point $F$, find the length of $FD$.
A) 3.4
B) 4.3
C) 5.2
D) 6.1

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