
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 $\begin{cases} x=2\cos \alpha \\ y=\sin \alpha\end{cases}$ ($\alpha$ is the parameter), in the polar coordinate system with the origin of the Cartesian coordinate system as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of line $l$ is $\rho\sin (\theta- \frac {\pi}{4})= \frac { \sqrt {2}}{2}$.  
$(1)$ Find the ordinary equation of curve $C$ in the Cartesian coordinate system and the inclination angle of line $l$;  
$(2)$ Let point $P(0,1)$, if line $l$ intersects curve $C$ at two different points $A$, $B$, find the value of $|PA|+|PB|$.

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