
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
Given a group of 15 pirates agree to divide a treasure chest of gold coins among themselves as follows, where the $k^{\text{th}}$ pirate to take a share takes $\frac{k}{15}$ of the coins that remain in the chest, determine the number of coins the 15th pirate receives if the number of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a whole number of coins.

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