
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 $\dfrac{CD}{DB}=\dfrac{2}{3}$ and $\dfrac{AF}{FB}=\dfrac{1}{3}$. Let $s = \dfrac{CQ}{QF}$ where $Q$ is the intersection point of $CF$ and $AD$. Find $s$.
[asy]
size(8cm); 
pair A = (0, 0), B = (9, 0), C = (3, 6); 
pair D = (6, 4), F = (6, 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);
[/asy]

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