
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
Dirlichlet was a famous German mathematician. The function $D(x)= \begin{cases} 1,x{\text{ is a rational number}} \\ 0,x{\text{ is an irrational number}}\end{cases}$ is known as the Dirichlet function. Five conclusions about the Dirichlet function $D(x)$ are given below:

$①$ If $x$ is an irrational number, then $D(D(x))=0$;

$②$ The range of the function $D(x)$ is $[0,1]$;

$③$ The function $D(x)$ is an even function;

$④$ If $T\neq 0$ and $T$ is a rational number, then $D(x+T)=D(x)$ holds for any $x∈R$;

$⑤$ There exist three different points $A(x_{1},D(x_{1}))$, $B(x_{2},D(x_{2}))$, $C(x_{3},D(x_{3}))$, such that $\triangle ABC$ is an equilateral triangle.

The sequence numbers of the correct conclusions are _______.

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