
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 \(ABC\), \(D\) lies on \(\overline{BC}\) and \(F\) lies on \(\overline{AB}\). Let \(\overline{AD}\) and \(\overline{CF}\) intersect at \(P\). Additionally, let \(E\) be a point on \(\overline{AC}\) such that \(\overline{BE}\) intersects \(\overline{CF}\) at \(Q\).

\[ \text{If } AP:PD = 3:4 \text{ and } FQ:QC = 3:2, \text{ find the ratio } \frac{AF}{FB}. \]

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