
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
Captain Charlie and First Mate Fred divide their bounty using the following scheme: Charlie says, "One for me, one for you," giving himself one coin and starting Fred's pile with one coin. They continue, "Two for me, and two for you," giving himself two more coins but making Fred's pile two coins in total. They pronounce, "Three for me, three for you," and so on, incrementally until Charlie eventually gives himself $x$ more coins while adjusting Fred's pile to just precisely $x$ coins in total. At the end of the division, Charlie has five times as many coins as Fred. Determine how many gold coins they had initially.

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