
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 \\(t < 0\\), let the function \\(f(x) = x^{3} + \dfrac{3(t-1)}{2}x^{2} - 3tx\\).
\\((1)\\) If \\(f(x)\\) has no extremum in \\((0,2)\\), find the value of \\(t\\);
\\((2)\\) If there exists \\(x_{0} \in (0,2)\\) such that \\(f(x_{0})\\) is the maximum value of \\(f(x)\\) on \\([0,2]\\), find the range of \\(t\\);
\\((3)\\) If \\(f(x) \leqslant xe^{x} - m\\) (where \\(e\\) is the base of the natural logarithm) holds for any \\(x \in [0,+\infty)\\) when the maximum value of \\(m\\) is \\(0\\), find the range of \\(t\\).

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