
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 $\lfloor a \rfloor$ denote the greatest integer less than or equal to $a$. Then, for the function $y = x - \lfloor x \rfloor$ ($x \in \mathbb{R}$), the following statements are made: (1) It has a maximum and a minimum value; (2) It is a periodic function; (3) It is an increasing function; (4) It is an even function.  
Among these, the correct ones are (fill in the corresponding numbers).

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