
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 equations of the curve $C\_1$ are given by $\begin{cases}x=\sqrt{2}\sin(\alpha+\frac{\pi}{4}) \\ y=\sin 2\alpha+1\end{cases}$ (where $\alpha$ is a parameter). In the polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis, the curve $C\_2$ has equation $\rho^2=4\rho\sin\theta-3$.

(1) Find the Cartesian equation of the curve $C\_1$ and the polar equation of the curve $C\_2$.
(2) Find the minimum distance between a point on the curve $C\_1$ and a point on the curve $C\_2$.

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