
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 equations of curve $C$ are $\left\{\begin{array}{l}{x=1+2\cos\varphi}\\{y=\sqrt{3}+2\sin\varphi}\end{array}\right.$ ($\varphi$ is the parameter), with the origin as the pole and the positive x-axis as the polar axis. The polar equation of the ray $l_{1}$ is $\theta =\alpha (0 \lt \alpha\ \ \lt \frac{π}{4})$, and the polar equation of the ray $l_{2}$ is $\theta =\alpha +\frac{π}{2}$.<br/>$(Ⅰ)$ Determine the type of curve $C$ and find its polar equation;<br/>$(Ⅱ)$ If the ray $l_{1}$ intersects curve $C$ at points $O$ and $A$, and the ray $l_{2}$ intersects curve $C$ at points $O$ and $B$, find the range of values for the area of $\triangle OAB$.

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