
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 $f(x)=|x-2|$.  
(I) If the solution set of the inequality $f(x-a+2)+f(x-1)\geqslant 4$ ($a < 3$) is $\{x|x\leqslant \frac {1}{2}$ or $x\geqslant \frac {9}{2}\}$, find the value of the real number $a$;  
(II) If for $\forall x\in \mathbb{R}$, $f(x-a+2)+2f(x-1)\geqslant 1$, find the range of values for the real number $a$.

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