
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
C. In a polar coordinate system, the pole is the origin of the Cartesian coordinate system, and the polar axis is the positive half-axis of the \\(x\\)-axis. It is known that the polar equation of curve \\(C\\) is \\(\rho=8\cos \theta\\).  
\\((1)\\) Find the Cartesian equation of curve \\(C\\);  
\\((2)\\) Suppose a line \\( \begin{cases} x=t+2 \\ y=t \end{cases} \\) (with \\(t\\) as the parameter) intersects curve \\(C\\) at points \\(A\\) and \\(B\\), find the length of \\(AB\\).

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