
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 side lengths $AB = 40$, $AC = 20$, and triangle area $200$. Let $D$ be the point on $\overline{AB}$ such that $AD = 10$ and $DB = 30$, and let $E$ be the point on $\overline{AC}$ such that $AE = 5$ and $EC = 15$. The angle bisector of $\angle BAC$ intersects $\overline{DE}$ at point $F$ and $\overline{BC}$ at point $G$. Determine the area of triangle $AFG$.
A) 80.0
B) 82.5
C) 84.4
D) 85.0

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