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

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

(II) Given that $f(x)$ attains a maximum at $x = 1$, determine the range of values for the real number $a$.

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