
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 $f(x) = \sqrt{|x+1| + |x-m| - 5}$ ($m > 0$), its domain is $\mathbb{R}$.

(Ⅰ) Find the range of the real number $m$.

(Ⅱ) If $a, b \in \mathbb{R}$, and $a+b+m=4$, $a^2+b^2+m^2 = 16$, find the value of the real number $m$.

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