
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
The function $f(x)=\sin x-\sqrt{3}\cos x$, among the following properties,

 $①x=\dfrac{\pi }{6}$ is a symmetry axis of its graph;    $②$The maximum value is $2$, and the amplitude is $4$;

 $③$An increasing interval is $\left[-\dfrac{\pi }{6},\dfrac{5\pi }{6}\right]$;    $④$One of its zeros is $\dfrac{4\pi }{3}$;

The correct sequence number(s) is/are __________.

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