
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
Consider the graph of the rational function $\frac{r(x)}{s(x)}$. Assume $s(x)$ is a quadratic polynomial, $r(4) = 4$, and $s(1) = 1$. Determine $r(x) + s(x)$, knowing there are horizontal and vertical asymptotes at $y=0$ and $x=2$ respectively, and a hole in the graph at $x=3$.

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