
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
Dirichlet, a famous German mathematician, defined a function $D(x) = \begin{cases} 1, & \text{if } x \text{ is rational} \\ 0, & \text{if } x \text{ is irrational} \end{cases}$, which is known as the Dirichlet function. Below are five statements about the Dirichlet function $D(x)$:
1. If $x$ is irrational, then $D(D(x)) = 0$;
2. The range of function $D(x)$ is $[0, 1]$;
3. The function $D(x)$ is an even function;
4. If $T \neq 0$ and $T$ is rational, then $D(x+T) = D(x)$ holds true for any $x \in \mathbb{R}$;
5. There exist three distinct points $A(x_1, D(x_1))$, $B(x_2, D(x_2))$, and $C(x_3, D(x_3))$ such that $\triangle ABC$ is an equilateral triangle.

The correct statements are numbered \_\_\_\_\_\_.

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