
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 function $f(x)=-x^{2}+ax+2(x^{2}-x)\ln x$.
(I) When $a=2$, find the monotonic intervals of $f(x)$;
(II) If $x\in(0,+\infty)$, find the minimum integer value of $a$ such that $f(x)+x^{2} > 0$ always holds.

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