
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
Let \\(a > 0\\) and the function \\(f(x)=\dfrac{1}{2}{{x}^{2}}-(a+1)x+a\ln x\\).

\\((1)\\) When \\(a=2\\), find the slope of the tangent line to the curve \\(y=f(x)\\) at the point \\((3,f(3))\\).

\\((2)\\) Find the extreme points of the function \\(f(x)\\).

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