
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 $f(x)= \sqrt {|x+2|+|x-4|-m}$, its domain is $\mathbb{R}$.  
(I) Find the range of the real number $m$;  
(II) If the maximum value of $m$ is $n$, when the positive numbers $a$, $b$ satisfy $\frac {4}{a+5b}+ \frac {1}{3a+2b}=n$, find the minimum value of $4a+7b$.

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