
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 $A$ and $B$, find the value of $|PA|+|PB|$.

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