
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
Alicia and Florent play the following game: starting with a number \(1 < n \leq 1000\), they each take turns playing by the following rules: Alicia (who starts) can either add 4 to the number (regardless of its current value) or divide it by 2 if it is even. Florent can either subtract 2 from the number (regardless of its current value) or multiply it by 2 if it is odd. Alicia wins if the number reaches 0 or 1, while Florent wins if the number exceeds 1000 or if Alicia has not won after 100 turns (one turn consists of both players having played once). Who has a winning strategy?

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