
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
In the polar coordinate system, the coordinates of point $P$ are $(1,0)$, and the equation of curve $C$ is $ρ=2 \sqrt {2}\cos (θ- \dfrac {π}{4})$. Establish a rectangular coordinate system on the plane with the pole as the coordinate origin and the positive half of the $x$-axis as the polar axis. The line $l$ with a slope of $-1$ passes through point $P$.
(1) Write the parametric equation of line $l$ and the rectangular coordinate equation of curve $C$;
(2) If line $l$ intersects curve $C$ at two points $A$, $B$, find the value of $|PA|^{2}+|PB|^{2}$.

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