
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 set $A=\{x|(x-6)(x-2a-5) > 0\}$, and the set $B=\{x|[(a^{2}+2)-x]\cdot(2a-x) < 0\}$.  
$(1)$ If $a=5$, find the intersection of set $A$ and $B$;  
$(2)$ Given $a > \dfrac {1}{2}$ and "if $x \in A$" is a necessary but not sufficient condition for "$x \in B$", find the range of the real number $a$.

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