
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 different way this time. Pete announces, "One for me, one for you," giving himself one coin and starting Paul's pile with one coin. He then says, "Two for me, two for you," adding two more coins to his total and bringing Paul's pile up to two coins in total. He continues with "Three for me, three for you," and so on, until Pete gives himself $x$ more coins while equalizing Paul's total to $x$ coins. When all coins are shared, Pirate Pete has exactly five times as many coins as Pirate Paul. How many gold coins did they share in total?

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