
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
A group of $15$ pirates agree to divide a treasure chest of gold coins among themselves differently: the $k^{\text{th}}$ pirate takes $\frac{k}{15}$ of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which this arrangement allows each pirate to receive a positive whole number of coins. Find the number of coins the $15^{\text{th}}$ pirate receives.
A) 720
B) 1296
C) 1728
D) 87,178,291,200
E) 3850

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