
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 for curve $C$ are 
\begin{cases}
x=3\cos \alpha\\ 
y=\sin \alpha 
\end{cases} (\alpha \text{ 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 for line $l$ is $p\sin \left(\theta- \dfrac{\pi}{4}\right)= \sqrt{2}$.
(1) Find the standard equation of $C$ and the inclination angle of $l$;
(2) Let point $P(0,2)$ be given, with $l$ intersecting $C$ at points $A$ and $B$. Find $|PA|+|PB|$.

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