
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} $ ($t$ is the parameter), establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is $ρ=2\cos (θ- \frac {π}{4})$.
(1) Find the slope angle of line $l$ and the rectangular coordinate equation of curve $C$;
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, and point $P(0, \frac{ \sqrt {2}}{2})$, find $|PA|+|PB|$.

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