
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
Given that there are 50 students, a majority of whom bought the same number of pens, each of these students purchased more than one pen, and the cost of each pen in cents was greater than the number of pens bought by each student, determine the cost of one pen in cents, given that the total amount spent on pens was 2310 cents.

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