
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, A and B, take turns removing stones from a pile of $n$ stones according to the following rules: Player A goes first, must take at least 1 stone, but cannot take all the stones. After that, each player can take up to the number of stones taken by the previous player, but must take at least one stone. The player who takes the last stone wins. For each $n \geqslant 2$, determine who has a winning strategy.

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