
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 $f(x)=x^{2}+ax-\ln x (a\in R)$.
(I) When $a=1$, find the monotonic interval of the function $f(x)$;
(II) Let $g(x)=f(x)-x^{2}$, does there exist a real number $a$ such that when $x\in(0,e]$, the minimum value of the function $g(x)$ is $3$? If so, find the value of $a$; if not, explain why.

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