
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 sets $M=\{x|x^{2}-x-2 < 0\}$ and $N=\{x|a < x < b, x\in\mathbb{R}, a,b\in\mathbb{R}\}$.  
$(1)$ Find the set $M$;  
$(2)$ If $M \supseteq N$, find the minimum value of $a$;  
$(3)$ If $M \cap N = M$, find the range of values for $b$.

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