
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 $g(x)=|x|+2|x+2-a| (a\in R)$.
(1) When $a=3$, solve the inequality $g(x)\leqslant 4$;
(2) Let $f(x)=g(x-2)$, find the range of real number $a$ such that $f(x)\geqslant 1$ holds true on $R$.

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