
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
Let the domain of the function $y=f(x)$ be $D$. If for any $x_{1} \in D$, there exists $x_{2} \in D$ such that $f(x_{1}) \cdot f(x_{2}) = 1$, then the function $f(x)$ is said to have property $M$. The following four statements are given:<br/>① The function $y=x^{3}-x$ does not have property $M$;<br/>② The function $y=\frac{{e^x}+{e^{-x}}}{2}$ has property $M$;<br/>③ If the function $y=\log _{8}(x+2), x \in [0,t]$ has property $M$, then $t=510$;<br/>④ If the function $y=\frac{{3\sin x+a}}{4}$ has property $M$, then $a=5$.<br/>The correct statement numbers are ____.

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