
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
There are \( n \) disks of different radii stacked on peg \( A \) from largest at the bottom to smallest at the top. Each move allows transferring a disk to either peg \( B \) or peg \( C \), but you cannot place a larger disk on top of a smaller disk. Design a method to transfer all \( n \) disks from peg \( A \) to peg \( C \), and estimate the number of moves required. You may use three pegs: \( A \), \( B \), and \( C \).

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