
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 a circle \\({x}^{2}+{y}^{2}+2ax-2ay+2{a}^{2}-4a=0(0 < a \leqslant 4)\\) with center \\(C\\), and a line \\(l\\): \\(y=x+4\\).  
\\((1)\\) Write down the coordinates of the center of the circle and its radius;  
\\((2)\\) Find the maximum length of the chord cut by the circle \\(C\\) from line \\(l\\).

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