
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 Cartesian coordinate system $xoy$, there is a line $l$: $x+y-2=0$. In the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the curve $C_{1}$: $\rho=1$. By stretching all the points on the curve $C_{1}$, making the $x$-coordinates $2 \sqrt {2}$ times longer and the $y$-coordinates $2$ times longer, we obtain the curve $C_{2}$. The line $l$ intersects the curve $C_{2}$ at points $A$ and $B$.  
$(1)$ Find the Cartesian coordinate equation of the curve $C_{2}$;  
$(2)$ Given the point $P(2,0)$, find the value of $\dfrac {1}{|PA|}+ \dfrac {1}{|PB|}$.

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