
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 a majority of the $30$ students in Ms. Demeanor's class bought pencils at the school bookstore, where each student bought the same number of pencils greater than $1$, and the total cost of all the pencils was $\$17.71$, determine the cost of a pencil in cents.

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