
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
Ana and Bernardo are playing the following game. They start with a bag containing $n \geq 1$ stones. Taking turns and starting with Ana, each player can make the following moves: if the number of stones in the bag is even, the player can take either one stone or half of the stones. If the number of stones in the bag is odd, the player must take one stone. The objective of the game is to take the last stone. Determine for which values of $n$ Ana has a winning strategy.

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