
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 the functions $f(x)=x\ln x$ and $g(x)=-x^{2}+ax-3$,  
(I) Find the intervals of monotonicity and the minimum value of the function $f(x)$;  
(II) If for all $x\in(0,+\infty)$, $2f(x)\geqslant g(x)$ always holds, find the range of the real number $a$.

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