
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 $a \in R$, and $f(x) = |x-a| + (1-a)x$.  
$(I)$ Solve the inequality for $a$: $f(2) < 0$;  
$(II)$ If $f(x) \geqslant 0$ holds for all $x$, find the range of the real number $a$.

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