
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 $f(x)$ with domain $\mathbb{R}$, and for any $x \in \mathbb{R}$, $f(x + 2) - f(x) = 0$. When $x \in [-1, 1)$, $f(x) = x$. Consider the following four statements about the function $f(x)$:
1. The function $f(x)$ is an odd function;
2. The function $f(x)$ is a periodic function;
3. All zeros of the function $f(x)$ are $x = 2k$, where $k \in \mathbb{Z}$;
4. When $x \in [-3, 3)$, the graph of the function $g(x) = \frac{1}{x}$ has exactly three points in common with the graph of the function $f(x)$.

The sequence numbers of all true statements are __________.

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