
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 $\begin{cases}x=3\cos α \\\\ y=\sin α\end{cases} (α\text{ is the parameter})$. 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 $ρ\sin \left(θ- \dfrac{π}{4}\right)= \sqrt{2}$.

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

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

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