
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) = x^2^ - xlnx,
(I) Find the equation of the tangent line to the curve y = f(x) at the point (1, f(1));
(II) If $$\frac{k}{x}$$ + $$\frac{x}{2}$$ - $$\frac{f(x)}{x}$$ < 0 holds true for all x in (1, +∞), find the range of the real number k.

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