
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 the curve $C$ is given by $\begin{cases} x=2\cos\theta \\ y=\sin\theta \end{cases}$ (where $\theta$ is the parameter). A line $l$ with slope $\alpha$ passes through the point $P(0, \sqrt{2})$.

1. Find the Cartesian equation of curve $C$ and the parametric equation of line $l$.
2. If line $l$ intersects curve $C$ at two distinct points $M$ and $N$, find the maximum value of $|PM| + |PN|$.

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