
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 $f(x)=|x-a|-1$, where $a > 1$.  
(I) When $a=2$, solve the inequality $f(x)\geqslant 4-|x-4|$.  
(II) Given that the solution set of the inequality $|f(2x+a)-2f(x)|\leqslant 1$ with respect to $x$ is $\{x| \frac {1}{2}\leqslant x\leqslant 1\}$, find the value of $a$.

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