
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 the coordinate origin $O$ as the pole and the non-negative semi-axis of the $x$-axis as the polar axis. The polar coordinates of point $P$ are given as $(2, \frac{\pi}{2})$, and the polar equation of curve $C$ is $\rho\cos \theta-\rho\sin \theta=1$. The parametric equations of curve $D$ are given as $\begin{cases} x=1+\cos \alpha \\ y=\sin \alpha \end{cases}$ ($\alpha$ is the parameter). The curves $C$ and $D$ intersect at points $A$ and $B$.
(1) Find the rectangular coordinates of point $P$;
(2) Find the rectangular equation of curve $C$ and the ordinary equation of curve $D$;
(3) Find the area $S$ of triangle $PAB$.

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