
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 $CE$ and $AD$ are drawn such that $\frac{CD}{DB} = \frac{5}{3}$ and $\frac{AE}{EB} = \frac{7}{3}$. Find $r = \frac{CQ}{QE}$ where $Q$ is the intersection of lines $CE$ and $AD$. 
[asy] size(8cm); pair A = (0, 0), B = (12, 0), C = (4, 8); pair D = (10, 2), E = (10, 0); pair Q = intersectionpoints(A--D, C--E)[0]; draw(A--B--C--cycle); draw(A--D); draw(C--E); label("$A$", A, SW); label("$B$", B, SE); label("$C$", C, N); label("$D$", D, NE); label("$E$", E, S); label("$Q$", Q, SE); //Credit by role specification[/asy]

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