
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 $A={x|x^{2}-ax+a^{2}-19=0}$, $B={x|x^{2}-5x+6=0}$, $C={x|x^{2}+2x-8=0}$, if $A \cap B \supset \varnothing$, $A \cap C = \varnothing$, find the value(s) of $a$.

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