
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
Triangle $ABC$ has sides $AB = 40$, $AC = 20$, and area $150$. Points $D$ and $E$ are midpoints of $\overline{AB}$ and $\overline{AC}$, respectively. The angle bisector of $\angle BAC$ intersects $\overline{DE}$ at $F$ and $\overline{BC}$ at $G$. Calculate the area of quadrilateral $FDBG$.
A) 70
B) 75
C) 80
D) 85

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