
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 $f(x) = ax^2 + (b-8)x - a - ab$, the solution set of $f(x) > 0$ is $(-3, 2)$,
(1) Find the expression of $f(x)$;
(2) When $x > -1$, find the maximum value of $$y= \frac {f(x)-21}{x+1}$$;
(3) If the solution set of the inequality $ax^2 + kx - b > 0$ is $A$, and $(1, 4) \subseteq A$, find the range of the real number $k$.

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