
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 $(xOy)$, the parametric equation of circle $C_{1}$ is given by $\begin{cases} x=1+\cos \phi \\ y=2+\sin \phi \end{cases}(\phi \text{ is a parameter})$, and the polar coordinate system is established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of line $C_{2}$ is $\rho\cos \theta+2=0$.
(1) Find the polar coordinate equation of $C_{1}$ and the rectangular coordinate equation of $C_{2}$;
(2) If the polar coordinate equation of line $C_{3}$ is $\theta= \frac {\pi}{4}(\rho\in\mathbb{R})$, let the intersection points of $C_{3}$ and $C_{1}$ be $M$, $N$, and $P$ be a point on $C_{2}$, such that the area of $\triangle PMN$ is equal to $1$, find the rectangular coordinates of point $P$.

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