
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 curve $C\_1$ are given by $\begin{cases}x=\cos \alpha \ y=\sqrt{3}\sin \alpha \end{cases} (\alpha$ is the parameter$), and the polar coordinate equation of curve $C\_2$ with the coordinate origin as the pole and the positive semiaxis of $x$ as the polar axis is $\rho\cos (\theta- \frac {\pi}{4})=3 \sqrt {2}$.
(1) Write the Cartesian equation of $C\_1$ and the rectangular coordinate equation of $C\_2$.
(2) If point $P$ is on $C\_1$ and point $Q$ is on $C\_2$, find the minimum value of $|PQ|$ and the rectangular coordinates of $P$ in this case.

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