
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) = $\sqrt{|x+2|+|6-x|-m}$, whose domain is R,

(I) Find the range of the real number m;

(II) If the maximum value of the real number m is n, and the positive numbers a and b satisfy $\frac{8}{3a+b}$ + $\frac{2}{a+2b}$ = n, find the minimum value of 2a + $\frac{3}{2}$b.

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