
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 rectangular coordinate system $xOy$, the parametric equation of line $l$ is given by $\begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$ ($t$ is a parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is given by $\rho^2 = \frac{4}{1+3\sin^2\theta}$.
(1) Find the ordinary equation of line $l$ and the rectangular coordinate equation of curve $C$.
(2) If there are exactly 2 points on curve $C$ that are $\sqrt{2}$ units away from line $l$, find the slope of line $l$.

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