
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= \frac { \sqrt {2}t}{2}+1 \\ y=- \frac { \sqrt {2}t}{2} \end{cases} (t \text{ is the parameter}) $, with the origin as the pole and the positive semi-axis of $x$ as the polar axis, and using the same unit length to establish the polar coordinate system, the polar coordinate equation of circle $C$ is $ρ=2 \sqrt {2}\cos (θ+ \frac {π}{4})$.

(1) Find the ordinary equation of line $l$ and the rectangular coordinate equation of circle $C$;
(2) Suppose circle $C$ intersects line $l$ at points $A$ and $B$, and point $P$ has rectangular coordinates $(1,0)$, find the value of $|PA|+|PB|$.

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