
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 symbol $[x]$ represents the largest integer not exceeding $x$, such as $[2.3]=2$, $[-1.3]=-2$. If the function $f(x)=x+[x]$ is defined, then among the following statements, all incorrect statements are numbered as:

① The domain of the function $f(x)$ is $\mathbb{R}$;  
② The range of the function $f(x)$ is $\mathbb{R}$;  
③ The function $f(x)$ is an odd function;  
④ The function $f(x)$ is a periodic function;  
⑤ The function $f(x)$ is an increasing function on $\mathbb{R}$.

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