
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 $ABC$, points $D$ and $E$ lie on side $\overline{BC}$, and point $F$ lies on side $\overline{AB}$. Lines $\overline{AD}$ and $\overline{CF}$ intersect at point $P$. Point $G$ lies on $\overline{AC}$, and line $\overline{BG}$ intersects $\overline{AD}$ at point $Q$.

Given that:
- $AP:PD = 3:2$
- $FP:PC = 2:1$
- $BQ:QG = 1:3$

Find $\frac{AF}{FB}$.

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