
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 $AG$ are drawn so that $\dfrac{CG}{GB}=\dfrac{4}{1}$ and $\dfrac{AF}{FB}=\dfrac{3}{1}$. Let $s=\dfrac{CQ}{QF}$ where $Q$ is the intersection point of $CF$ and $AG$. Determine the value of $s$.
[asy] size(8cm); pair A = (0, 0), B = (12, 0), C = (4, 8); pair G = (10, 2), F = (9, 0); pair Q = intersectionpoints(A--G, C--F)[0]; draw(A--B--C--cycle); draw(A--G); draw(C--F); label("$A$", A, SW); label("$B$", B, SE); label("$C$", C, N); label("$G$", G, NE); label("$F$", F, S); label("$Q$", Q, S); [/asy]

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