
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 $f(x)=|x+m|+|2x-1|$ where $m\in\mathbb{R}$.

(I) When $m=-1$, find the solution set of the inequality $f(x)\leqslant 2$.

(II) Let $A$ be the solution set of the inequality $f(x)\leqslant |2x+1|$ regarding $x$, and $[1,2]\subseteq A$. Find the range of the real number $m$.

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