
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 $f(x)=|2x|+|2x+3|+m$, where $m\in\mathbb{R}$.  
(I) When $m=-2$, find the solution set of the inequality $f(x)\leqslant 3$;  
(II) For all $x\in(-\infty, 0)$, if $f(x)\geqslant x+ \frac{2}{x}$ always holds, find the range of $m$.

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