
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
[Elective 4-4: Coordinate Systems and Parametric Equations]

In the rectangular coordinate system $xOy$, the curve $C\_1$ is defined by the parametric equations $\begin{cases} x=3\cos \theta \ y=\sin \theta \end{cases}$ (where $\theta$ is a parameter), and in the polar coordinate system with $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis, the curve $C\_2$ is defined by the equation $\rho(\cos \theta-\sin \theta)=4$.

(1) Write the ordinary equations of the curves $C\_1$ and $C\_2$;
(2) If there is a moving point $M$ on the curve $C\_1$ and a moving point $N$ on the curve $C\_2$, find the coordinates of point $M$ when $|MN|$ is minimum.

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