
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
Yatta and Yogi play a game in which they begin with a pile of  $n$  stones.  The players take turns removing  $1$ ,  $2$ ,  $3$ ,  $5$ ,  $6$ ,  $7$ , or  $8$  stones from the pile.  That is, when it is a player's turn to remove stones, that player may remove from  $1$  to  $8$  stones, but *cannot* remove exactly  $4$  stones.  The player who removes the last stone *loses*.  Yogi goes first and finds that he has a winning position, meaning that so long as he plays perfectly, Yatta cannot defeat him.  For how many positive integers  $n$  from  $100$  to  $2008$  inclusive is this the case?

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