
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 $f(x) = x^2 - bx + 3$, and $f(0) = f(4)$.  
(1) Find the zeros of the function $y = f(x)$, and write the set of $x$ values for which $f(x) < 0$;  
(2) Find the maximum and minimum values of the function $y = f(x)$ in the interval $[0, 3]$.

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