
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
Given a function $y=f(x)$ defined on $\mathbb{R}$ that satisfies the condition $f\left(x+\frac{3}{2}\right)=-f(x)$, and the function $y=f\left(x-\frac{3}{4}\right)$ is an odd function. Consider the following four statements:

① The function $f(x)$ is a periodic function;  
② The graph of the function $f(x)$ is symmetric about the point $\left(-\frac{3}{4}, 0\right)$;  
③ The function $f(x)$ is an even function;  
④ The function $f(x)$ is monotonic on $\mathbb{R}$.  

Among these four statements, the correct ones are __________ (write down the numbers of all correct statements).

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