
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 $f(x)=|x+m|+|2x-1|$ $(m\in \mathbb{R})$  
$(I)$ When $m=-1$, solve the inequality $f(x)\leqslant 2$;  
$(II)$ Let the solution set of the inequality $f(x)\leqslant |2x+1|$ with respect to $x$ be $A$, and $[\frac{3}{4},2]\subseteq A$, find the range of the real number $m$.

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