
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 $(xOy)$, establish a polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar coordinate equation of the curve $C_{1}$ is $ρ=2 \sqrt {2}\sin (θ+ \dfrac {π}{4})$, and the parametric equation of the line $l$ is $ \begin{cases} x=1- \dfrac { \sqrt {2}}{2}t \\ y= \dfrac { \sqrt {2}}{2}t\end{cases}(t\text{ is the parameter}) $. The line $l$ intersects the curve $C_{1}$ at points $A$ and $B$.
(I) Find the length of $|AB|$;
(II) If the parametric equation of the curve $C_{2}$ is $ \begin{cases} x=3+ \sqrt {2}\cos α \\ y=4+ \sqrt {2}\sin α\end{cases}(α\text{ is the parameter}) $, and $P$ is any point on the curve $C_{2}$, find the minimum value of the area of $\triangle PAB$.

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