
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 $f(x)=x\ln x-ax^{2}+(2a-1)x$, where $a > 0$.
(I) Let $g(x)=f′(x)$, find the monotonic intervals of $g(x)$;
(II) If $f(x)$ takes the maximum value at $x=1$, find the range of the real number $a$.

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