
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 functions $f(x)=|x-2|$ and $g(x)=m|x|-2$ ($m\in\mathbb{R}$).  
$(1)$ Solve the inequality $f(x) > 3$ with respect to $x$.  
$(2)$ If the inequality $f(x) \geqslant g(x)$ holds for any $x\in\mathbb{R}$, find the range of values for $m$.

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