
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 $A=\{x|x^{2} - 5x + 6 = 0\}$, $B=\{x|x^{2} - ax + 18 = 0\}$, and $C=\{x|x^{2} + 2x - 8 = 0\}$, such that $A \cap B \neq \emptyset$ and $B \cap C = \emptyset$,  
(1) List the elements of sets A and C.  
(2) Find the value of $a$.

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