
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 $f(x)=|kx-1|$.

(I) If the solution set of $f(x)\leqslant 3$ is $[-2,1]$, find the value of the real number $k$.

(II) When $k=1$, if the inequality $f(x+2)-f(2x+1)\leqslant 3-2m$ holds for any $x\in \mathbb{R}$, find the range of the real number $m$.

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