
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
Given the parametric equations of line $l$ as $ \begin{cases} x= \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t \end{cases} (t \text{ is the parameter}) $, and the parametric equations of curve $C$ as $ \begin{cases} x= \sqrt {2}+2\cos θ \\ y=2 \sqrt {2}+2\sin θ \end{cases} $, $(θ \text{ is the parameter})$. In a polar coordinate system established with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis, the polar coordinates of point $P$ are $(3 \sqrt {2}, \frac {π}{2})$.
(I) Find the polar equations of line $l$ and curve $C$;
(II) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the area of triangle $PAB$.

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