
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 set $A_{0}=\{x\left|\right.0 \lt x \lt 1\}$. For a function $y=f\left(x\right)$, define set $A_{n}=\{y|y=f\left(x\right)$, $x\in A_{n-1}\}$. If $A_{n}\cap A_{n-1}=\varnothing $ holds for any $n\in N^{*}$, then the function $y=f\left(x\right)$ is said to have the property "$\varphi $".<br/>Given the following functions:<br/>①$y=\frac{1}{x}$;<br/>②$y=x^{2}+1$;<br/>③$y=x$;<br/>④$y=2^{x}$.<br/>The numbers of functions that have the property "$\varphi $" are______.

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