
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
Joel wishes to arrange his marbles into X groups, each containing an equal number of marbles, Y. Each group will have more than one marble, but not all marbles will be in one group. If there are 17 possible values for Y given all the restrictions, what is the smallest number of marbles he could have?

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