
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 and Pirate Polly decide to share a treasure. Pete starts by saying, "One for me, one for you," giving himself one coin and starting Polly's pile with one coin. The pattern continues with Pete saying, "Two for me, two for you," giving himself two more coins but making Polly's pile two coins in total. This continues until Pete says "$x$ for me, $x$ for you," where he has given himself $x$ more coins, and Polly's pile is $x$ coins in total. At this distribution point, Pirate Pete has exactly three times as many coins as Pirate Polly. How many gold coins do they have in total?

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