
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 $|x+2|+|6-x| \geq k$ always holds true.  
(1) Find the maximum value of the real number $k$;  
(2) If the maximum value of the real number $k$ is $n$, and the positive numbers $a$, $b$ satisfy $\frac {8}{5a+b}+ \frac {2}{2a+3b}=n$, find the minimum value of $7a+4b$.

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