
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
Suppose the function $f(x) = x - |x+2| - |x-3| - m (m \in \mathbb{R})$.

(I) When $m=-4$, find the maximum value of the function $f(x)$.

(II) If there exists $x_0 \in \mathbb{R}$ such that $f(x_0) \geq \frac{1}{m} - 4$, find the range of values for the real number $m$.

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