
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 universal set $U=\mathbb{R}$, let the set $A=\{x|(x-2)(x-3)<0\}$, and the domain of the function $y=\log \frac{x-(a^{2}+2)}{a-x}$ is set $B$.
(1) If $a=\frac{1}{2}$, find the set $A\cap(\complement_{U}B)$;
(2) Let proposition $P$: $x\in A$, and proposition $Q$: $x\in B$. If $Q$ is a necessary condition for $P$, find the range of the real number $a$.

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