
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) = 2x ln(x) - a, where a ∈ R,

(I) Find the extreme values of the function f(x);

(II) If the inequality e^x f(x) - x^2 - 1 ≥ 0 holds true for any real number x ≥ 1, find the range of values for the real number a.

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