
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 are $n$ balls. Players A and B take turns picking balls without putting them back. Each time, they pick at least 1 ball and at most 3 balls. The player who picks the last ball wins. If A goes first, the correct inference is _____ (fill in the number).
① If $n=4$, A has a winning strategy.
② If $n=6$, B has a winning strategy.
③ If $n=9$, A has a winning strategy.
④ If $n=11$, B has a winning strategy.

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