
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
Given the polar equation of curve \\(C_1\\) is \\(\rho +6\sin \theta +\dfrac{8}{\rho }=0\\), with the pole \\(O\\) as the origin of the Cartesian coordinate system and the polar axis as the positive half-axis of \\(x\\), establish a Cartesian coordinate system in the plane \\(xoy\\), where the equation of curve \\(C_2\\) is \\(\dfrac{x^2}{5}+y^2=1\\).

\\((\\)I\\()\\) Write the Cartesian coordinate equation of \\(C_1\\) and the parametric equation of \\(C_2\\);

\\((\\)II\\()\\) Let \\(M,N\\) be any points on \\(C_1\\) and \\(C_2\\) respectively, find the maximum value of \\(\left| MN \right|\\).

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