
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) = ax^2 - (2a + 1)x + lnx (a ∈ R)
(I) Find the monotonic intervals of function f(x) when a > 0.
(II) Let g(x) = f(x) + 2ax. If g(x) has two extreme points x1, x2, and the inequality g(x1) + g(x2) < λ(x1 + x2) always holds, find the range of the real number λ.

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