
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 $M=\{x|(x+3)(x-5)>0\}$, $P=\{x|x^2+(a-8)x-8a\leq0\}$.  
(1) Find a value of $a$ that makes it a sufficient but not necessary condition for $M \cap P = \{x|5<x\leq8\}$.  
(2) Find a range of values for $a$ that makes it a necessary but not sufficient condition for $M \cap P = \{x|5<x\leq8\}$.

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