
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
- **New Problem Statement**:
  Lora wants to arrange her set of coins into $X$ piles, each containing an equal number of coins, $Y$. Every pile must have more than two coins, and no single pile should contain all the coins. If there are 17 possible values for $Y$, given all these conditions, what is the smallest number of coins she could have?

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