
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 $ABC$ with $AB = 60$ and $AC = 30$ has an area of $180$ units. Let $D$ and $E$ be points on $AB$ and $AC$ such that $AD = 20$ and $AE = 10$. The angle bisector of $\angle BAC$ intersects line segments $DE$ and $BC$ at points $F$ and $G$, respectively. Determine the area of quadrilateral $FDBG$.
A) $125$ 
B) $130$
C) $130\frac{6}{7}$
D) $135$

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