
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 on a plane, the curve $C\_1$: $\begin{cases} x=2+2\cos \alpha \\ y=\sin \alpha \end{cases}$ ($\alpha$ is a parameter) undergoes a transformation to become curve $C\_2$ as follows: $\begin{cases} x'=\frac{x}{2} \\ y'=y \end{cases}$. Using the origin $O$ as the pole and the non-negative x-axis as the polar axis, establish the polar coordinate system.

(I) Find the polar equation of the curve $C\_2$;

(II) Points $A$ and $B$ are on curve $C\_2$ and $∠AOB=\frac{π}{3}$, find the range of $|OA|=|OB|$.

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