
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
Two players play a game on a pile of  $n$  beans. On each player's turn, they may take exactly  $1$ ,  $4$ , or  $7$  beans from the pile. One player goes first, and then the players alternate until somebody wins. A player wins when they take the last bean from the pile. For how many  $n$  between  $2014$  and  $2050$  (inclusive) does the second player win?

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