
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 quadratic function $f(x)$ passes through points $A(-1, 0)$, $B(3, 0)$, and $C(1, -8)$,  
(1) Find the expression of $f(x)$;  
(2) Find the maximum and minimum values of $f(x)$ on the interval $[0, 3]$;  
(3) Find the solution set of the inequality $f(x) \geq 0$.

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