
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
Alice and Bob play the following game: Alice picks a set  $A = \{1, 2, ..., n \}$  for some natural number  $n \ge 2$ . Then, starting from Bob, they alternatively choose one number from the set  $A$ , according to the following conditions: initially Bob chooses any number he wants, afterwards the number chosen at each step should be distinct from all the already chosen numbers and should differ by  $1$  from an already chosen number. The game ends when all numbers from the set  $A$  are chosen. Alice wins if the sum of all the numbers that she has chosen is composite. Otherwise Bob wins. Decide which player has a winning strategy.

Proposed by *Demetres Christofides, Cyprus*

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