
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 $f(x)=3\cos (2x+ \frac {π}{6})(x∈R)$, determine the correct statement(s) from the following options:
$①$ If $|f(x_{1})|=|f(x_{2})|=3$ and $x_{1}≠ x_{2}$, then $x_{1}-x_{2}$ must be an integer multiple of $π$;
$②$ The graph of $y=f(x)$ is symmetric about the point $(\frac {π}{6},0)$;
$③$ The graph of $y=f(x)$ is symmetric about the line $x= \frac {π}{3}$;
$④$ The expression of $y=f(x)$ can be rewritten as $y=3\sin (2x- \frac {π}{3})$;
$⑤$ The function $y=f(x)$ is increasing on the interval $[- \frac {π}{3},- \frac {π}{6}]$.

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