
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
Suppose (4-4): Coordinate Systems and Parametric Equations

In the rectangular coordinate system $xOy$, the parametric equations of the curve $C$ are $\begin{cases} x=3\cos \alpha \\ y=\sin \alpha \end{cases}$, where $\alpha$ is the parameter. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of the line $l$ is $\rho \sin (\theta - \frac{\mathrm{\pi }}{4})=\sqrt{2}$.

(I) Find the ordinary equation of $C$ and the slope angle of the line $l$;

(II) Let point $P(0,2)$, and $l$ intersects $C$ at points $A$ and $B$. Find $|PA|+|PB|$.

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