
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
Five sailors landed on an island and gathered a pile of coconuts by evening. They decided to divide the coconuts in the morning. One of them woke up during the night, gave one coconut to a monkey, and took exactly one-fifth of the remaining coconuts for himself, then went back to sleep. Throughout the night, each of the other sailors did the same, not knowing about the others' actions. In the morning, they divided the remaining coconuts equally, and this time there was no extra coconut for the monkey. What could be the smallest number of coconuts in the pile?

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