
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
Determine whether the following statements about functions and their extreme values are correct (denoted by "√") or incorrect (denoted by "×").

(1) The maximum value of a function is always greater than the minimum value. $\quad$ ( )

(2) If the derivative of a function is 0 at a point, then that point is an extreme value. $\quad$ ( )

(3) Every function $y = f(x)$ has a maximum value and a minimum value. $\quad$ ( )

(4) If a function has an extreme value in a given interval, then the extreme value point must be inside the interval. $\quad$ ( )

(5) The extreme value point of a function is the value of the independent variable, and the extreme value is the function value. $\quad$ ( )

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