
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
In the long development of mathematics, mathematicians have discovered the mysterious phenomenon of "black holes" in mathematics. Mathematical black hole: no matter how the values are set, under the specified processing rules, a fixed value will eventually be obtained, and it will not be able to escape, just like a black hole in the universe. The discovered number black holes include the "$123$ black hole," "Kaprekar black hole," "narcissistic number black hole," etc. Definition: If the sum of the $n$th power of the digits of an $n$-digit positive integer is equal to the number itself, then this number is called a narcissistic number. It is known that the set $A$ consists of all one-digit positive integers that are narcissistic numbers, and the set $B=\{x|\frac{{x}^{2}-5x-3}{2-x}＜1,x∈{N}^{*}\}$. Then the number of non-empty subsets in $A\cap B$ is ______.

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