
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(x+1)lnx - x + 1, where a belongs to the set of real numbers,

1. Find the equation of the tangent line to f(x) at the point (1, f(1)) when a = 2.
2. Determine the range of values for 'a' such that f(x) is non-negative for all x in the interval [1, +∞).

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