
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 universal set $U=\mathbb{R}$, let $A=\{x|x^2+(a-1)x-a>0\}$ and $B=\{x|(x+a)(x+b)>0\}$ where $a \neq b$. Also define $M=\{x|x^2-2x-3 \leq 0\}$.
1. If the complement of $B$ with respect to $U$, $\bar{B}$, equals $M$, find $a$ and $b$;
2. If $-1 < b < a < 1$, find $A \cap B$.

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