
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
Let $x \in \mathbb{R}$, and use $[x]$ to represent the greatest integer less than or equal to $x$, for example, $[-1.5]=-2$, $[5.1]=5$. Then, among the following properties of the function $f(x)=[x]$, the correct statements are \_\_\_\_\_\_ . (Fill in the correct numbers) ① The domain is $\mathbb{R}$, the range is $\mathbb{Z}$; ② If $x_1 \leq x_2$, then $[x_1] \leq [x_2]$; ③ $[n+x]=n+[x]$, where $n \in \mathbb{Z}$; ④ $[x] \leq x < [x]+1$; ⑤ $$[-x]= \begin{cases} -[x]-1  (x \notin \mathbb{Z}) \\ -[x]   (x \in \mathbb{Z})\end{cases}$$

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