
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 set $A=\{x|x^2-ax-2=0\}$, and the set $B=\{x|x^3+bx+c=0\}$, and $-2 \in A \cap B$, $A \cap B = A$, find the values of the real numbers $a$, $b$, $c$.

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