
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 polar coordinate system, the equation of curve $C\_1$ is $ρ=2\sin (θ+ \frac{π}{3})$, and the equation of curve $C\_2$ is $ρ\sin (θ+ \frac{π}{3})=4$. Establish a rectangular coordinate system $xOy$ with the pole $O$ as the origin and the polar axis direction as the positive direction of the $x$-axis.
(1) Find the rectangular coordinate equations of curves $C\_1$ and $C\_2$;
(2) Let $A$ and $B$ be moving points on $C\_1$ and $C\_2$ respectively, find the minimum value of $|AB|$.

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