
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 $(xOy)$, a polar coordinate system is established with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of circle $C$ is $ρ=2 \sqrt {2}\cos (θ+ \dfrac {π}{4})$, and the parametric equation of line $l$ is $ \begin{cases} \overset{x=t}{y=-1+2 \sqrt {2}t}\end{cases}(t\text{ is the parameter})$. Line $l$ intersects circle $C$ at points $A$ and $B$, and $P$ is any point on circle $C$ different from $A$ and $B$.
(I) Find the polar coordinates of the circle center;
(II) Find the maximum area of $\triangle PAB$.

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