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

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