
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) = alnx + be^(x-1) - (a+2)x + a (where e is the base of the natural logarithm, and a, b are constants with a, b belonging to the set of real numbers)

1. Discuss the monotonicity of the function f(x) in the interval (1, +∞) when a=0.
2. When b=2, if f(x) ≥ 0 holds for any x in the interval [1, +∞), find the range of values for the real number a.

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