
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 Qingqing Grassland, there are 7 sheep numberd  $1,2,3,4,5,6,7$  and 2017 wolves numberd  $1,2,\cdots,2017$ . We have such strange rules:
(1) Define  $P(n)$ : the number of prime numbers that are smaller than  $n$ . Only when  $P(i)\equiv j\pmod7$ ,  wolf  $i$  may eat sheep  $j$  (he can also choose not to eat the sheep).
(2) If wolf  $i$  eat sheep  $j$ , he will immediately turn into sheep  $j$ .
(3) If a wolf can make sure not to be eaten, he really wants to experience life as a sheep.
Assume that all wolves are very smart, then how many wolves will remain in the end?

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