
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 Cartesian coordinate system $xOy$, the parametric equation of curve $C_{1}$ is $\begin{cases} & x=2+2\cos \alpha , \\ & y=2\sin \alpha , \end{cases}$ ($\alpha$ is the parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established, and the polar equation of curve $C_{2}$ is $\rho=2\cos \theta$.

(Ⅰ) Write the ordinary equation of curve $C_{1}$ and the Cartesian coordinate equation of curve $C_{2}$;

(Ⅱ) Suppose point $P$ is on $C_{1}$, point $Q$ is on $C_{2}$, and $\angle POQ=\frac{\pi}{2}$, find the maximum area of triangle $POQ$.

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