
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 $A=\{x|x^2+(4-a^2)x+a+3=0\}$, $B=\{x|x^2-5x+6=0\}$, $C=\{x|2x^2-5x+2=0\}$.
(1) If $A \cap B = A \cup B$, find the value of $a$;
(2) If $A \cap B = A \cap C \neq \emptyset$, find the value of $a$.

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