
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 equations of line $l$ as $\begin{cases}x=t, \\\\ y= \frac{ \sqrt{2}}{2}+ \sqrt{3}t\end{cases} $ where $t$ is the parameter, and a curve $C$ with the polar coordinate equation $\rho=2\cos (θ- \frac{π}{4} )$ is established using the origin $O$ of the rectangular coordinate system as the pole and the $ox$ direction as the polar axis with the same unit length.

(1) Find the angle of inclination 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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