
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 rectangular coordinate system $(xOy)$, with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar coordinate equation of the curve $C_{1}$ is $ρ=2 \sqrt{2}\sin \left(θ+ \dfrac{π}{4}\right)$, 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) The rectangular coordinate equations of the curve $C_{1}$ and the line $L$;

(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 and maximum values of the area of $\triangle PAB$.

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