
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
The correct numbers among the following propositions are ______.<br/>① The function $f\left(x\right)=a^{x-1}+3\left(a \gt 1\right)$ is increasing on $R$;<br/>② If the domain of the function $f\left(x-1\right)$ is $\left(1,3\right)$, then the domain of the function $f\left(x\right)$ is $\left(2,4\right)$;<br/>③ Given $f\left(x\right)=x^{5}+ax^{3}+bx-8$, and $f\left(-2\right)=8$, then $f\left(2\right)=-8$;<br/>④ $f\left(x\right)=\frac{1}{1-{2}^{x}}-\frac{1}{2}$ is an odd function.

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