
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 $f: \mathbf{N}_{+} \rightarrow A$ with the following property: if $i, j \in \mathbf{N}_{+}$ and the absolute difference $|i-j|$ is a prime number, then $f(i) \neq f(j)$. What is the minimum number of elements in the set $A$?

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