
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 \\(f(x)=x\ln x\\) and \\(g(x)=-x^{2}+ax-3\\).

\\((1)\\) Find the minimum value of the function \\(f(x)\\) on the interval \\((0,e]\).

\\((2)\\) For all \\(x \in (0,+\infty)\\), if \\(2f(x) \geqslant g(x)\\) holds, find the range of the real number \\(a\\).

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