
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
For a finite set \( A \), there exists a function \( f: \mathbb{N} \rightarrow A \) with the following property: if \( |i-j| \) is a prime number, then \( f(i) \neq f(j) \), where \( \mathbb{N} = \{1, 2, 3, \ldots\} \). Find the minimum number of elements in the finite set \( A \).

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