
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 Paul have found another stash of coins. This time, Pete decides to distribute the coins according to a modified pattern. Initially, Pete says, "One for me, none for you," starting his pile with one coin while Paul's pile remains empty. Then Pete proceeds, “Two for me, one for you,” giving himself two more coins and putting one coin in Paul's pile. Next, Pete declares, "Three for me, one for you," adding three coins to his pile and one more to Paul’s pile. This continues until Pete decides he will give himself \(x\) more coins and make Paul’s pile equal to \(\frac{x}{3}\) in total. By the end, Pete has exactly five times as many coins as Pirate Paul. How many coins do they have in total?

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