
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 $C\_1$ are given by $\begin{cases} x=2\cos \phi \\ y=\sin \phi \end{cases}$ (where $\phi$ is the parameter), and in the polar coordinate system with pole $O$ and polar axis as the positive half of the $x$-axis, curve $C\_2$ is a circle with center $(3, \frac{\pi}{2})$ and radius $1$.

1. Find the Cartesian equations of curves $C\_1$ and $C\_2$.
2. Let $M$ be a point on curve $C\_1$ and $N$ a point on curve $C\_2$. Determine the range of values for $|MN|$.

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