
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 curve $C:x^{2}+y^{2}=1$ undergoes a transformation $\varphi :\begin{cases} & x'=\sqrt{3}x \\ & y'=y \\ \end{cases}$ to obtain the curve $(C_{1})$. In the polar coordinate system established with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of the curve $(C_{2})$ is $\rho \sin (\theta + \frac{\pi }{4})=4\sqrt{2}$.

(1) Find the parametric equation of the curve $(C_{1})$ and the rectangular coordinate equation of the curve $(C_{2})$;

(2) Let $P$ be a moving point on the curve $(C_{1})$, find the minimum value of the distance from point $P$ to a point on $(C_{2})$, and the coordinates of point $P$ at this time.

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