
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 plane rectangular coordinate system $(xOy)$, establish a polar coordinate system $(.$ with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. If the polar coordinate equation of the line $l$ is $\sqrt {2}ρ\cos (θ- \dfrac {π}{4})-2=0$, and the polar coordinate equation of the curve $C$ is: $ρ\sin ^{2}θ=\cos θ$, shrink the abscissa of all points on the curve $C$ to half of the original, and the ordinate remains unchanged. Then, translate it to the right by one unit to obtain the curve $C_{1}$.
(I) Find the rectangular coordinate equation of the curve $C_{1}$;
(II) It is known that the line $l$ intersects with the curve $C_{1}$ at points $A$ and $B$. Point $P(2,0)$, find the value of $(|PA|+|PB|)$.

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