
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 sets $M=\{x|x < -3\}$ or $x > 5\}$, $P=\{x|(x-a)\cdot(x-8)\leqslant 0\}$.
$(1)$ Find the necessary and sufficient condition for $M\cap P=\{x|5 < x\leqslant 8\}$;
$(2)$ Find a value of the real number $a$ that makes it a sufficient but not necessary condition for $M\cap P=\{x|5 < x\leqslant 8\}$.

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