
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 in an intricate way. Pete begins by saying, "One for me, one for you," giving himself one coin and starting Paul's pile with one coin. Then Pete says, "Three for me, one for you," adding three more coins to his own pile but making Paul's pile two coins in total. The pattern continues as "Five for me, one for you," and so on, increasing the number of coins Pete takes by two each round, but only adding one coin to Paul's pile each time. This continues until Pete gives himself $2x-1$ more coins and makes Paul's pile $x$ coins in total. At this point, all of the coins have been distributed, and Pirate Pete has exactly three times as many coins as Pirate Paul. Determine the total number of coins they have.

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