
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 - 12 = 0\} $, and set $ B = \{x | x^2 + bx + c = 0\} $, with the condition that $ A \neq B $ and $ A \cup B = \{-3, 4\} $, $ A \cap B = \{-3\} $. Find the real numbers $ b $ and $ c $.

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