
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 a line $l$ with the parametric equations $\begin{cases}x= \dfrac{ \sqrt{2}t}{2}+1 \\ y=- \dfrac{ \sqrt{2}t}{2}\end{cases}$ (where $t$ is the parameter), and using the Cartesian origin as the pole with the positive $x$-axis as the polar axis, and adopting the same unit for length in the polar coordinate system, the polar equation of circle $C$ is $\rho=2 \sqrt {2}\cos (\theta+ \dfrac {π}{4})$.
(1) Determine the standard equation of line $l$ and the Cartesian equation for circle $C$;
(2) Assuming circle $C$ intersects line $l$ at points $A$ and $B$, and point $P$ has Cartesian coordinates $(1,0)$, find the value of $|PA|+|PB|$.

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