
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 $\triangle ABC$, lines $CF$ and $AD$ are drawn such that $\dfrac{CD}{DB}=\dfrac{2}{1}$ and $\dfrac{AF}{FB}=\dfrac{5}{3}$. Determine $s=\dfrac{CQ}{QF}$ where $Q$ is the intersection point of $CF$ and $AD$.
[asy] size(8cm); pair A = (0, 0), B = (9, 0), C = (3, 6); pair D = (6, 2), F = (6.75, 0); pair Q = intersectionpoints(A--D, C--F)[0]; draw(A--B--C--cycle); draw(A--D); draw(C--F); label("$A$", A, SW); label("$B$", B, SE); label("$C$", C, N); label("$D$", D, NE); label("$F$", F, S); label("$Q$", Q, S); //Credit for the asymptote[/asy]

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