
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
Let $a$ be a real number, and the function $f(x) = (x-a)^2 + |x-a| - a(a-1)$.
1. If $f(0) \leq 1$, find the range of values for $a$;
2. Discuss the monotonicity of $f(x)$;
3. When $a > 2$, discuss the number of zeros of $f(x) + |x|$ on $\mathbb{R}$.

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