
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, with the origin \\(O\\) as the pole and the positive half-axis of the \\(x\\)-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve \\(C\\) is \\(\rho=4\cos \theta\\), and the rectangular coordinate equation of curve \\(M\\) is \\(x-2y+2=0\\) (\\(x > 0\\)).

    \\((1)\\) Using the slope \\(k\\) of the line connecting points on curve \\(M\\) to point \\(O\\) as a parameter, write the parametric equation of curve \\(M\\);

    \\((2)\\) Suppose the two intersection points of curve \\(C\\) and curve \\(M\\) are \\(A\\) and \\(B\\), find the sum of the slopes of lines \\(OA\\) and \\(OB\\).

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