
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 - $\frac{\ln{x}}{x}$ - a, where a ∈ R.

1. If x = 1 is the extreme point of f(x), find the value of a and discuss the monotonicity of f(x).
2. If 1 < x < e and f(x) ≤ 0, find the range of values for a.

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