
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
Three children, \( A \), \( B \), and \( C \), are playing a skill game. They agree that the loser of each round will give each of the other two players a number of marbles equal to twice the number of marbles they currently have, tripling the other players' marble count. After three rounds, which were successively lost by \( A \), \( B \), and \( C \), each player ends up with the same number of marbles. How many marbles did each player have originally if, after the first game, \( C \) had 54 more marbles than \( A \)?

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