
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: $f(x)=ax^2+(b-8)x-a-ab$, when $x \in (-3,2)$, $f(x) > 0$; when $x \in (-\infty,-3) \cup (2,+\infty)$, $f(x) < 0$

$(1)$ Find the explicit formula for $y=f(x)$

$(2)$ For what value of $c$, the solution set of $ax^2+bx+c \leq 0$ is $\mathbb{R}$.

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