
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 Patty decide to share a hoard of treasure. Pete starts by saying, "One for me, one for you," giving himself one coin and starting Patty's pile with one coin. He continues this pattern by doubling the previous round's allocation, saying, "Two for me, and two for you," giving himself two more coins but making Patty's pile two coins in total. This pattern continues until Pete gives himself $x$ more coins, but makes Patty’s pile $x$ coins in total. Finally, all the coins are distributed, and Pirate Pete has exactly five times as many coins as Pirate Patty. How many gold coins do they have in total?

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