
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 given by $\begin{cases} x=3\cos \alpha \\ y=\sin \alpha \end{cases}$ ($\alpha$ is the parameter). In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of the line $l$ is given by $\rho \sin \left( \theta -\dfrac{\pi }{4} \right)=\sqrt{2}$.

(1) Find the Cartesian equation of $C$ and the angle of inclination of $l$;

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

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