
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 $f(x)=| x-a |$, where $a > 1$

(I) When $a=2$, find the solution set of the inequality $f(x) \geqslant 4-| x-4 |$.

(II) Given that the solution set of the inequality $| f(2x+a)-2f(x) | \leqslant 2$ with respect to $x$ is $\{ x|1\leqslant x\leqslant 2 \}$, find the value of $a$.

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