
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) = alnx - x^2 + (2a - 1)x, where a ∈ R.
(I) Find the monotonic intervals of the function f(x) when a = 1;
(II) Find the extreme values of the function f(x);
(III) If the function f(x) has two different zero points, find the range of a.

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