
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) = (2ax - ln x) ln x - 2ax + 2.
1. Find the equation of the tangent line to the curve y = f(x) at the point (1, f(1)) when a = 1.
2. Determine the range of values for the real number a such that f(x) ≥ 0 for any x ∈ [1, +∞).

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