
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 $f(x) = x^2 + bx + c$, and $f(1) = 0$, $f(3) = 0$,
(1) Find the value of $f(-1)$;
(2) Find the maximum and minimum values of $f(x)$ when $x \in [2, 4]$;
(3) Determine the monotonicity of $f(x)$ on $[2, +\infty)$.

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