
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 $A={x|x^{2}+ax+12b=0}$ and $B={x|x^{2}-ax+b=0}$, where $2 \in (\neg_{U}A) \cap B$ and $4 \in A \cap (\neg_{U}B)$, with $U=\mathbb{R}$, find the values of the real numbers $a$ and $b$.

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