
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
There is a strip of graph paper with 15 cells, numbered $0,1,2, \ldots, 14$. Two players take turns moving a token, which is on one of the cells, to the left by 1, 2, or 3 spaces. The player who has no moves loses. For which starting positions of the token does the first player win, and for which positions does the second player win?

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