
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 a slightly different manner. This time, Pete says, "One for me, one for you," giving himself one coin and starting Paul's pile with one coin. Then he says, "Three for me, two for you," giving himself three more coins but making Paul's pile two coins in total. Next, Pete says, "Six for me, three for you," and so on, increasing the number he takes by three each time and Paul's pile by one each time. This pattern continues until Pete gives himself $3x$ more coins but makes Paul's pile $x$ coins in total. At this point, all of the coins have been distributed, and Pirate Pete has exactly six times as many coins as Pirate Paul. How many gold coins do they have in total?

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