
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
Pirate Pete shares his treasure with Pirate Paul, but this time in a slightly different manner. Pete starts by saying, "One for me, one for you," giving himself one coin and starting Paul's pile with one coin. He then says, "Two for me, and two for you," giving himself two more coins but making Paul's pile two coins in total. The pattern continues with Pete announcing, "Three for me, three for you," and so forth, until Pete gives himself $x$ more coins making Paul’s pile $x$ coins in total. They continue this process until all the coins are distributed, with Pirate Pete having exactly three times as many coins as Pirate Paul. Determine the total number of gold coins they have.

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