
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 $f(x) = ax + \frac{b}{x} - 2a + 2$ (where $a > 0$), the tangent line to the graph at the point $(1, f(1))$ is parallel to the line $y = 2x + 1$.
(I) Find the value of $\log_{4}(a - b)$;
(II) If the inequality $f(x) - 2\ln x \geq 0$ holds true for $x \in [1, +\infty)$, determine the range of values for $a$.

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