
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 functions f(x) = lnx - 2ax + 2a and g(x) = xf(x) + ax^2 - x (where a ∈ R),
(I) Find the monotonic intervals of function f(x);
(II) If function g(x) attains its maximum value at x = 1, find the range of positive real number a.

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