
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 maximum integer not exceeding $x$, such as $[π]=3$, $[-1.08]=-2$. The function $\{x\}$ is defined as $\{x\}=x-[x]$. Provide the correct proposition number for the following four propositions:

① The domain of function $\{x\}$ is R, and its range is $[0, 1]$

② The equation $\{x\}=\frac{1}{2}$ has infinite solutions

③ Function $\{x\}$ is an odd function

④ Function $\{x\}$ is an increasing function

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