
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
On the vast grassland, there are 7 sheep numbered 1, 2, 3, 4, 5, 6, and 7, and 2017 wolves numbered 1, 2, 3, ..., 2017. The grassland follows these peculiar rules:
(1) Define \(P(n)\) as the number of prime numbers less than \(n\). Wolf numbered \(i\) can eat sheep numbered \(j\) if and only if \(P(i) \equiv j \pmod{7}\) (eating is optional);
(2) If the wolf numbered \(i\) eats the sheep numbered \(j\), it immediately transforms into the sheep numbered \(j\);
(3) Each wolf wants to experience life as a sheep, provided it ensures that it will not be eaten thereafter.

Assuming each wolf is very clever, determine how many wolves will remain on the grassland in the end.

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