
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
Let the function be $f(x)=|x+2|-|x-1|$.
- $(1)$ Find the solution set of the inequality $f(x) > 1$;
- $(2)$ If the inequality $f(x)+4\geqslant |1-2m|$ has a solution with respect to $x$, find the range of the real number $m$.

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