
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 set $A=\{x|x^2-ax+a^2-19=0\}$, $B=\{x|x^2-5x+6=0\}$, $C=\{x|x^2+2x-8=0\}$ satisfy $A \cap B \neq \emptyset$ and $A \cap C = \emptyset$. Find the value of the real number $a$.

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