
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 the Cartesian coordinate system $(xOy)$, the parametric equations of the curve $C$ are $\begin{cases} x=2\cos \theta, \\ y=4\sin \theta \end{cases} (\theta \text{ is the parameter})$, and the parametric equations of the line $l$ are $\begin{cases} x=1+t\cos \alpha, \\ y=2+t\sin \alpha \end{cases} (t \text{ is the parameter})$.

(1) Find the Cartesian equations of $C$ and $l$;

(2) If the midpoint of the line segment obtained by intersecting the curve $C$ and the line $l$ has coordinates $(1, 2)$, find the slope of $l$.

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