
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) = e^x(-x + lnx + a), where e is the base of the natural logarithm, a is a constant, and a ≤ 1.
(I) Determine whether the function f(x) has an extreme value point in the interval (1, e), and explain the reason.
(II) If a = ln2, find the minimum integer value of k such that f(x) < k is always true.

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