
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 curve $C_1$ is represented by the parametric equations:
$$
\begin{cases}
x = 2\cos \phi \\
y = \sin \phi
\end{cases}
$$
(where $\phi$ is a parameter). In the polar coordinate system with the origin O and the positive x-axis as the polar axis, the curve $C_2$ is a circle centered at $(3, \frac{\pi}{2})$ with radius 1.

(Ⅰ) Find the Cartesian equations of curves $C_1$ and $C_2$.
(Ⅱ) 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 length |MN|.

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