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

1. Find the Cartesian equation of curve $C\_1$ and the polar equation of curve $C\_2$.
2. Let $M$ be a point on curve $C\_1$, and $N$ be a point on curve $C\_2$. Find the range of values for the distance $|MN|$.

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