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

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

(Ⅱ) If there exists $x_{0}\in \mathbb{R}$ such that $f(x_{0})\geqslant \frac{1}{m}-4$, find the range of the real number $m$.

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