
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 given by \\( \begin{cases} x=\cos \theta \\ y=\sin \theta \end{cases} \\) with \\(\theta\\) as the parameter. By stretching all the x-coordinates and y-coordinates of points on \\(C_1\\) by \\( \sqrt{2} \\) and 2 times respectively, we obtain the curve \\(C_2\\). Using the origin \\(O\\) of the Cartesian coordinate system \\(xOy\\) as the pole and the positive x-axis as the polar axis, we establish a polar coordinate system with the same unit length. The line \\(l\\) is given by \\(\rho( \sqrt{2} \cos \theta + \sin \theta) = 4\\).
\\((1)\\) Write down the polar equations for the curve \\(C_1\\) and the parametric equations for the curve \\(C_2\\).
\\((2)\\) Find a point \\(P\\) on the curve \\(C_2\\) such that the distance from \\(P\\) to the line \\(l\\) is minimized, and calculate this minimum distance.

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