
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
For a function $f(x)$ defined on $\mathbb{R}$, consider the following five statements:

① If $y = f(x)$ is an odd function, then the graph of $y = f(x - 1)$ is symmetric about the point $A(1,0)$.

② If for any $x \in \mathbb{R}$, $f(x - 1) = f(x + 1)$ holds, then $f(x)$ is symmetric about the line $x = 1$.

③ The graphs of the functions $y = f(x + 1)$ and $y = f(1 - x)$ are symmetric about the line $x = 1$.

④ If the function $y = f(x)$ satisfies $f(x + 1) = f(1 - x)$ and $f(x + 3) = f(3 - x)$, then the function has a period of 4.

The correct statement(s) is/are numbered \_\_\_\_\_\_\_\_.

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