
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
On the board, there is an integer written. Two players, $A$ and $B$, take turns playing, starting with $A$. Each player, on their turn, replaces the existing number with the result of performing one of these two operations: subtracting 1 or dividing by 2, as long as the result is a positive integer. The player who reaches the number 1 wins. Determine, with reasoning, the smallest even number that requires $A$ to play at least 2015 times to win (excluding $B$'s turns).

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