
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
The parametric equations of curve $C\_1$ are: $\begin{cases} x=1+t\cos \frac{\pi }{4} \ y=5+t\sin \frac{\pi }{4} \end{cases} (t \text{ is the parameter})$, and the parametric equations of curve $C\_2$ are: $\begin{cases} x=\cos \phi \ y=\sqrt{3}\sin \phi \end{cases} (\phi \text{ is the parameter})$.
(1) Find the Cartesian equation of curve $C\_2$, and find the polar equation of curve $C\_1$ if the coordinate system is established with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis.
(2) If point $P$ is any point on curve $C\_2$, find the minimum distance from point $P$ to curve $C\_1$.

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