
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) = ln x + $\frac{1}{x}$ + ax, where x > 0, a ∈ R.
(I) Find the range of values for a such that the function f(x) is not monotonic in the interval [1, +∞).
(II) Find the value of a such that the function f(x) has a maximum value of $\frac{2}{e}$ in the interval [1, +∞).

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