
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
Performing the following action is called an operation: Cutting a rope of integer length into three ropes of integer lengths, with the condition that exactly one of them is the longest. Given a rope of length \( a^b \) (where \( a \) and \( b \) are integers greater than 1), two players, A and B, take turns performing the operation. Player A starts first. Each player operates on the longest rope obtained from the previous operation. If a player cannot perform the operation on their turn, the other player wins. Determine which player has a winning strategy.

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