
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 using a modified pattern. Pete initiates 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 and making Paul’s pile two coins in total. This pattern continues with Pete saying, "Three for me, three for you," and so on, until Pete gives himself $x$ more coins but makes Paul’s pile $x$ coins in total. When all coins are distributed, Pirate Pete has exactly five 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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