
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^2 - xlnx - (2a - 1)x + a - 1, where a ∈ R:
1. Find the equation of the tangent line to the function f(x) at point P(e, f(e)) when a = 0.
2. Determine the range of real values for 'a' such that the function f(x) ≥ 0 holds true for any x ∈ [1, +∞).

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