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

  
$(1)$ Find the general equation of curve $C$ and the inclination angle of line $l$;  

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

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