
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 $f(x) = ax^2 + a^2x + 2b - a^3$, for $x \in (-2, 6)$, we have $f(x) > 0$, and for $x \in (-\infty, -2) \cup (6, +\infty)$, we have $f(x) < 0$.
(1) Determine the explicit expression for $f(x)$.
(2) Find the maximum and minimum values of $f(x)$ on the interval $[1, 10]$.

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