
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
Cindy wishes to arrange her coins into \( X \) piles, each consisting of the same number of coins, \( Y \). Each pile will have more than one coin and no pile will have all the coins. If there are 15 possible values for \( Y \) given all of the restrictions, what is the smallest number of coins she could have?

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