
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 $P$ is $(1,0)$, and the equation of curve $C$ is $\rho =2\sqrt{2}\cos (\theta -\dfrac{\pi }{4})$. Establish a rectangular coordinate system with the pole as the coordinate origin and the positive semi-axis of the polar axis as the $x$-axis. A line $l$ with a slope of $-1$ passes through point $P$.

(I) Write the parametric equation of line $l$ and the rectangular coordinate equation of curve $C$;
(II) If line $l$ intersects curve $C$ at two points $A$ and $B$, find the value of $|PA{{|}^{2}}+|PB{{|}^{2}}$.

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