
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
Karen wants to arrange her chairs into \( X \) groups, each consisting of the same number of chairs, \( Y \). Each group will have more than one chair, and no group will have all the chairs. If there are 9 possible values for \( Y \) given all the conditions, what is the smallest number of chairs she could have?

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