
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 $a > 1$,
(1) When $a=2$, find the solution set for the inequality $f(x)\geqslant 4-|x-4|$;
(2) Given that the solution set of the inequality about $x$, $|f(2x+a)-2f(x)|\leqslant 2$, is $\{x|1\leqslant x\leqslant 2\}$, find the value of $a$.

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