
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 function $f(x) = ax^2 + (b-8)x - a - ab$, it has the property that $f(x) > 0$ when $x\in(-3, 2)$, and $f(x) < 0$ when $x\in(-\infty, -3) \cup (2, +\infty)$.  
(1) Find the explicit formula for $f(x)$.  
(2) If the solution set for the inequality $ax^2 + bx + c \leq 0$ is $\mathbb{R}$, find the range of possible values for $c$.  
(3) When $x > -1$, find the maximum value of $y = \frac{f(x) - 21}{x + 1}$.

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