
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
Let \\(f(x)=x\ln x-ax^{2}+(2a-1)x\\), where \\(a\in\mathbb{R}\\).
\\((\\)I\\()\\) Let \\(g(x)=f′(x)\\), find the intervals of monotonicity for \\(g(x)\\);
\\((\\)II\\()\\) Given that \\(f(x)\\) has a local maximum at \\(x=1\\), find the range of values for the real number \\(a\\).

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