
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) = \frac{1}{3}x^3 - \frac{1}{2}(a+1)x^2 + ax\\).

\\((1)\\) Find the intervals of monotonicity for the function \\(f(x)\\);

\\((2)\\) If \\(a > 1\\), and the maximum value of the function \\(y = f(x)\\) on the interval \\(\left[0, a+1\right]\\) is \\(f(a+1)\\), find the range of the real number \\(a\\).

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