
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 $f(x)=x\ln x–ax^{2}+(2a–1)x$, where $a\in R$.

(I) Let $g(x)=f'(x)$, find the monotonic intervals of $g(x)$;

(II) It is known that $f(x)$ takes the maximum value at $x=1$. Find the range of the real number $a$.

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