
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 a function $f(x)=ax^{2}-(a+2)x-b$ (where $a, b \in \mathbb{R}$).  
$(1)$ If the solution set of the inequality $f(x) > 0$ is $(-3,2)$, find the value of $a+b$;  
$(2)$ When $a \geq 0$ and $b=-2$, find the solution set of the inequality $f(x) \geq 0$.

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