
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 $f(x) = |x+3| - m + 1$, where $m > 0$, the solution set of $f(x-3) \geq 0$ is $(-\infty, -2] \cup [2, +\infty)$.  
(I) Find the value of $m$;  
(II) If there exists $x \in \mathbb{R}$ such that $f(x) \geq |2x-1| - t^2 + \frac{5}{2}t$ holds, find the range of the real number $t$.

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