
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 $\mathbb{R}$ satisfies the condition $f = -f(x)$, and the function $y = f$ 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 a point;  
(3) The function $f(x)$ is an even function on $\mathbb{R}$;  
(4) The function $f(x)$ is a monotonic function on $\mathbb{R}$.  
Among these statements, the true ones are numbered as \_\_\_\_\_\_\_\_. (Write down the numbers of all true statements)

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