
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
Choose one of the three conditions:①$A\cap B=\{3\}$, ②$A\cap B=\{6\}$, ③$A\cap B=\{3,6\}$, and supplement it into the following question. If the set $B$ exists in the question, find the value of $a$; if the set $B$ does not exist in the question, explain the reason.<br/>Question: Does there exist a set $B$ such that $A=\{1,3,a^{2}+3a-4\}$, $B=\{0,6,a^{2}+4a-2,a+3\}$, and ______$?$

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