
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 3 piles of stones. Each time, person A moves 1 stone from one pile to another. Each time A moves a stone, they receive a reward from person B. The amount of money A receives is equal to the difference between the number of stones in the pile to which they added the stone and the number of stones in the pile from which the stone was taken. If this difference is negative, person A must return that amount of money to person B (if A does not have enough money to return, they can owe it temporarily). After several moves, all the stones return to their original piles. Find the maximum amount of money A can earn.

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