
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 equations of the curve $C$ are $x=3\cos \alpha$ and $y=\sin \alpha$ ($\alpha$ is the parameter). In the polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of the line $l$ is $\rho \sin (\theta -\frac{\pi }{4})=\sqrt{2}$.

1. Find the ordinary equation of the curve $C$ and the rectangular coordinate equation of the line $l$.
2. Let point $P(0, 2)$. The line $l$ intersects the curve $C$ at points $A$ and $B$. Find the value of $|PA|+|PB|$.

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