
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 that the function $y=f(x)$ is an odd function defined on $\mathbb{R}$ and satisfies $f(x-1)=f(x+1)$ for all $x \in \mathbb{R}$. When $x \in (0,1]$ and $x_1 \neq x_2$, we have $\frac{f(x_2) - f(x_1)}{x_2 - x_1} < 0$. Determine the correct statement(s) among the following:

(1) $f(1)=0$

(2) $f(x)$ has 5 zeros in $[-2,2]$

(3) The point $(2014,0)$ is a symmetric center of the function $y=f(x)$

(4) The line $x=2014$ is a symmetry axis of the function $y=f(x)$

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