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

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