
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 $a$ is a real number, and the function $f(x) = (x-a)^2 + |x-a| - a(a-1)$.  
(Ⅰ) If $f(0) \leq 1$, find the range of values for $a$;  
(Ⅱ) When $a \geq 2$, discuss the number of zeros of $f(x) + \frac{4}{x}$ in the interval $(0, +\infty)$.

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