
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
For the function $f(x)$, with the domain $D=[-2,2]$, which of the following statements is correct? (Fill in only the statement number)

$①$ If $f(-1)=f(1)$ and $f(-2)=f(2)$, then $y=f(x)$ is an even function on $D$  
$②$ If $f(-1) < f(0) < f(1) < f(2)$, then $y=f(x)$ is an increasing function on $D$  
$③$ If for all $x∈[-2,2]$, $f(-x)+f(x)=0$, then $y=f(x)$ is an odd function on $D$  
$④$ If the function $y=f(x)$ is monotonic on $D$ and $f(0) > f(1)$, then $y=f(x)$ is a decreasing function on $D$.

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