
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 $f(x)=|x-2m|-|x+m|$ where $(m > 0)$.  
$(1)$ When $m=2$, find the solution set of the inequality $f(x) \geqslant 1$;  
$(2)$ For any real numbers $x$, $t$, the inequality $f(x) \leqslant |t+3|+|t-2|$ always holds, find the range of values for $m$.

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