
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 $ABC$ with $AB = 40$ and $AC = 20$, the area is $160$. Let $D$ be the midpoint of $\overline{AB}$, and let $E$ be the point on $\overline{AC}$ such that $AE = 4EC$. The angle bisector of $\angle BAC$ intersects $\overline{DE}$ and $\overline{BC}$ at $F$ and $G$, respectively. What is the area of quadrilateral $FDBG$?
A) 110  
B) 120  
C) 124  
D) 130  
E) 135

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