
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) = xlnx - $\frac{ax^{2}}{2}$ + a - x (a ∈ R).

1. Find the range of values for the real number a if the function f(x) has two distinct extreme points.
2. If a = 2, k ∈ N, g(x) = 2 - 2x - x², and the inequality k(x - 2) + g(x) < f(x) always holds when x > 2, find the maximum value of k.

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