
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 $f(x)$ defined on $\mathbb{R}$, the correct statement(s) is/are \_\_\_\_\_\_.
$①$ If $f(-4)=f(4)$, then the function $f(x)$ is even.
$②$ If the function $f(x)$ is a strictly decreasing function on $\mathbb{R}$, then $f(-4) > f(4)$.
$③$ If the function $f(x)$ is odd, then $f(-4)+f(4)=0$.
$④$ If the function $f(x)$ is not a strictly increasing function on $\mathbb{R}$, then $f(-4)\geqslant f(4)$.

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