
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
Example 24 (Problem from the 2007 Bulgaria National Mathematics Competition): Two players, A and B, play the following game: Player A first takes a pile of \( n \) stones and divides it into three piles, each with at least one stone, ensuring that one of the piles has more stones than each of the other two piles. Then, Player B divides the pile with the most stones in the same manner. Players A and B take turns in this fashion. The player who makes the last move wins. For numbers of the form \( n = a^{b} \) (where \( a \) and \( b \) are integers greater than 1), which numbers allow Player B to have a winning strategy?

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