
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 $U=\mathbb{R}$, non-empty sets $A=\{x|\frac{x-2}{x-(3a+1)}<0\}$ and $B=\{x|\frac{x-a^{2}-2}{x-a}<0\}$.
(I) When $a=\frac{1}{2}$, find $\neg(B\cap A)$;
(II) Proposition $p$: $x\in A$, proposition $q$: $x\in B$. If $q$ is a necessary condition for $p$, find the range of values for the real number $a$.

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