
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
Find the least number of elements of a finite set  $A$  such that there exists a function  $f : \left\{1,2,3,\ldots \right\}\rightarrow A$  with the property: if  $i$  and  $j$  are positive integers and  $i-j$  is a prime number, then  $f(i)$  and  $f(j)$  are distinct elements of  $A$ .

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