
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
Given the parametric equation of line $l$ as $$\begin{cases} x=t \\ y= \frac { \sqrt {2}}{2}+ \sqrt {3}t \end{cases}$$  (where $t$ is the parameter), if the origin $O$ of the Cartesian coordinate system $xOy$ is taken as the pole and the direction of $Ox$ as the polar axis, and the same unit of length is chosen to establish the polar coordinate system, then the polar equation of curve $C$ is $\rho=2\cos\left(\theta- \frac {\pi}{4}\right)$.  
(1) Find the angle of inclination of line $l$ and the Cartesian equation of curve $C$;  
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, and let point $P(0, \frac { \sqrt {2}}{2})$, find $|PA|+|PB|$.

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