
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 \in \mathbb{R}\\), the function \\(f(x) = 2x^3 - 3(a+1)x^2 + 6ax\\).
\\((I)\\) If the function \\(f(x)\\) has an extremum at \\(x=3\\), find the equation of the tangent line to the curve \\(y=f(x)\\) at the point \\((0,f(0))\\).
\\((II)\\) If \\(a > \frac{1}{2}\\), and the minimum value of the function \\(y=f(x)\\) on the interval \\([0,2a]\\) is \\(-a^2\\), find the value of \\(a\\).

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