
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
Let the universal set $U = \mathbb{R}$, let $A = \{x|x^2 + px + 12 = 0\}$, and let $B = \{x|x^2 - 5x + q = 0\}$. If $\overline{A} \cap B = \{2\}$, and $A \cap \overline{B} = \{4\}$, find $A \cup B$.

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